# Aligning equation in align environment

I would like to fit the column and bring the equation to the left with equally spaced 'or'. Any suggestions how to go from here.

\documentclass{article}
\usepackage{amsmath,xcolor}

\begin{document}
\begin{align*}
&&&&&&&&    (3x-2)(2x^{2}-13x+15)&=0 &&  \\
&&&&&&&&        (3x-2)(2x-15)(x+1)&=0  && \color{blue}
{\text{Factor the trinomial}}\\
3x-2&=0 &&\text{or} & 2x-15&=0 &&\text{or} & x+1&=0 && \color{blue}
{\text{Set each factor to zero}} \\
3x&=2 &&\text{or} &  2x&=15 &&\text{or} &  x&=-1  &&
\color{blue}{\text{Solve}}\\
x&=\dfrac{2}{3} &&\text{or} &
x&=\dfrac{15}{2} &&  &  &  && \color{blue}{\text{}}\\
\end{align*}
\end{document}


Something like this?

\documentclass{article}
\usepackage{amsmath,xcolor}

\begin{document}
\begin{align*}
&&&&&&&&    \makebox[0pt][r]{$(3x-2)(2x^{2}-13x+15)$}&=0 &&  \\
&&&&&&&&        \makebox[0pt][r]{$(3x-2)(2x-15)(x+1)$}&=0  && \color{blue}
{\text{Factor the trinomial}}\\
3x-2&=0 &&\text{or} & 2x-15&=0 &&\text{or} & x+1&=0 && \color{blue}
{\text{Set each factor to zero}} \\
3x&=2 &&\text{or} &  2x&=15 &&\text{or} &  x&=-1  &&
\color{blue}{\text{Solve}}\\
x&=\dfrac{2}{3} &&\text{or} &
x&=\dfrac{15}{2} &&  &  &  && \color{blue}{\text{}}\\
\end{align*}
\end{document}


• Exactly what I needed. I didn't know those commands. Thanks for saving me time! – MathScholar Sep 26 '18 at 15:38