How to put a lot of equations in left side

I would like to put the following equations in the left side of my text, I do not know which command will be useful for that. I used align, but it put all equations in right most side of paper. More precisely, I want to put all of the equations below each other and their position be the left side of paper.

\begin{document}
\begin{align*}
(f,f)_{[x^3]_{1}}  = (f,f)_{[x^3]_{1}}=0 \\
(f,g)_{[x^3]_{1}} =(f,g)_{[x^3]_{3}}=0\\
(f,h)_{[xxy]_{1}}=(f,h)_{[xxy]_{3}}=0\\
(f,p)_{[xxy]_{1}}=(f,p)_{[xxy]_{3}}=0\\
(f,m)_{[xxt]_{1}}=[xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2})= [xtx]_{1}\\
(f,m)_{[xxt]_{3}}=[xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
(g,f)_{[x^3]_{1}}=(g,f)_{[x^3]_{3}}=0\\
\end{align*}
\end{document}
• you have used align but marked no alignment points (should be &=) but we can not run the code to see any problems as you only posted a fragment and you ask about text but the fragment has no text, if you want equations on the left, is it a two column document? Please edit your question – David Carlisle Aug 12 at 18:23
• You have to add an ampersand in each row in front of each alignment point (for instance, in front of the first = sign in each row). If you don't, it will be aligned by the end of each row. – Bernard Aug 12 at 18:24

The package nncmath provide environment fleqn which push equation to the left text border:

\documentclass{article}
\usepackage{nccmath}

%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\begin{document}

\begin{fleqn}
\begin{gather*}
(f,f)_{[x^3]_{1}}  = (f,f)_{[x^3]_{1}}=0 \\
(f,g)_{[x^3]_{1}} =(f,g)_{[x^3]_{3}}=0 \\
(f,h)_{[xxy]_{1}}=(f,h)_{[xxy]_{3}}=0 \\
(f,p)_{[xxy]_{1}}=(f,p)_{[xxy]_{3}}=0 \\
(f,m)_{[xxt]_{1}}=[xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2})= [xtx]_{1}\\
(f,m)_{[xxt]_{3}}=[xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
(g,f)_{[x^3]_{1}}=(g,f)_{[x^3]_{3}}=0\\
\end{gather*}
\end{fleqn}

\end{document} (red lines indicate text borders)

Here is a possible suggestion including three different alignments (red lines indicate margins): \documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{flalign*}
(f,f)_{[x^3]_{1}}  &= (f,f)_{[x^3]_{1}}=0 &&\\
(f,g)_{[x^3]_{1}} &=(f,g)_{[x^3]_{3}}=0 \\
(f,h)_{[xxy]_{1}}&=(f,h)_{[xxy]_{3}}=0 \\
(f,p)_{[xxy]_{1}}&=(f,p)_{[xxy]_{3}}=0 \\
(f,m)_{[xxt]_{1}}&=[xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2})= [xtx]_{1}\\
(f,m)_{[xxt]_{3}}&=[xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
(g,f)_{[x^3]_{1}}&=(g,f)_{[x^3]_{3}}=0\\
\end{flalign*}

\begin{align*}
(f,f)_{[x^3]_{1}}  &= (f,f)_{[x^3]_{1}}=0 \\
(f,g)_{[x^3]_{1}} &=(f,g)_{[x^3]_{3}}=0 \\
(f,h)_{[xxy]_{1}}&=(f,h)_{[xxy]_{3}}=0 \\
(f,p)_{[xxy]_{1}}&=(f,p)_{[xxy]_{3}}=0 \\
(f,m)_{[xxt]_{1}}&=[xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2})= [xtx]_{1}\\
(f,m)_{[xxt]_{3}}&=[xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
(g,f)_{[x^3]_{1}}&=(g,f)_{[x^3]_{3}}=0\\
\end{align*}

\begin{flalign*}
&(f,f)_{[x^3]_{1}}  = (f,f)_{[x^3]_{1}}=0 &&\\
&(f,g)_{[x^3]_{1}} =(f,g)_{[x^3]_{3}}=0 \\
&(f,h)_{[xxy]_{1}}=(f,h)_{[xxy]_{3}}=0 \\
&(f,p)_{[xxy]_{1}}=(f,p)_{[xxy]_{3}}=0 \\
&(f,m)_{[xxt]_{1}}=[xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2})= [xtx]_{1}\\
&(f,m)_{[xxt]_{3}}=[xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
&(g,f)_{[x^3]_{1}}=(g,f)_{[x^3]_{3}}=0\\
\end{flalign*}

\end{document}
• It solved my question, but the only problem is that in the margin, all $(f,f)$ are not written below each other completely and there exists small distances from red margin – user118746 Aug 12 at 18:33
• @user118746: I have added a third variant. – leandriis Aug 12 at 18:40

Just to add a little variant in which some equations are centered and others are aligned to the left, of course is not as elegant as @leandriis answer but it could be useful:

\documentclass{article}
\usepackage{amsmath}
\usepackage{blindtext}

\begin{document}

\begin{align*}
& (f,f)_{[x^3]_{1}} = (f,f)_{[x^3]_{1}}=0 \\
& (f,g)_{[x^3]_{1}} = (f,g)_{[x^3]_{3}}=0 \\
& (f,h)_{[xxy]_{1}} = (f,h)_{[xxy]_{3}}=0 \\
& (f,p)_{[xxy]_{1}} = (f,p)_{[xxy]_{3}}=0 \\
& (f,m)_{[xxt]_{1}} = [xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2}) = [xtx]_{1}\\
& (f,m)_{[xxt]_{3}} = [xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
& (g,f)_{[x^3]_{1}} =(g,f)_{[x^3]_{3}}=0\\
\end{align*}

%some blind text to check that margins are correct
\blindtext

\begin{align*}
& (f,f)_{[x^3]_{1}} = (f,f)_{[x^3]_{1}}=0 \\
& (f,g)_{[x^3]_{1}} = (f,g)_{[x^3]_{3}}=0 \\
\noalign{\hspace{-\parindent}$(f,h)_{[xxy]_{1}} = (f,h)_{[xxy]_{3}}=0$}
\noalign{\hspace{-\parindent}$(f,p)_{[xxy]_{1}} = (f,p)_{[xxy]_{3}}=0$}
& (f,m)_{[xxt]_{1}} = [xx]_{1} \dashv t  - x \dashv ([xt]_{1} - [tx]_{2}) = [xtx]_{1}\\
& (f,m)_{[xxt]_{3}} = [xx]_{1}\vdash t - x \vdash ([xt]_{1} - [tx]_{2})=[xxt]_3-[xxt]_2+[xtx]_3\\
& (g,f)_{[x^3]_{1}} =(g,f)_{[x^3]_{3}}=0\\
\end{align*}

\end{document}

And the output is: 