Aligning equations in columns

Question

as the title says, i wanna make three aligned colums of equations. First column being aligned left with the text above, second centered and last aligned right with the text. I am using align environment but the alignment doesn't look just right. I am really just a beginner at using LaTeX, so pardon me for trivial questions.

Answer 1

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

\begin{document}

\blindtext

% See also https://www.overleaf.com/learn/latex/Aligning_equations_with_amsmath,
%   https://tex.stackexchange.com/questions/239252, and
%   https://tex.stackexchange.com/questions/3782.

\begin{multline} % Remark: "multline" is written without an "i" after "mult".
p(x) = 3x^6 + 14x^5y + 590x^4y^2 + 19x^3y^3\\ 
- 12x^2y^4 - 12xy^5 + 2y^6 - a^3b^3\\
- 12x^2y^4 - 12xy^5 + 2y^6 - a^3b^3
\end{multline}

\blindtext

\end{document}

Answer 2

To have three columns in an equation, use groups separated by &. You can control if the whole equation environment is centred (align) or distributed over the page (flalign).

Just in case you would like a non-centred equation, you can also wrap flalign inside the minipage with calculated mandatory argument width and horizontal spacing.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage[nopar]{kantlipsum}
\usepackage{showframe}
    \renewcommand\ShowFrameLinethickness{0.2pt}
    \renewcommand\ShowFrameColor{\color{green}}
\begin{document}
\kant[1][1]
\begin{align}
  \alpha_i &= a_ib_j - \beta_i\gamma_j   &   \gamma_i &=r_i - r_j   &   a &= b + c + d + e\
  \alpha_j &= c - \beta_j                &   \gamma_j &=r_j - r_k   &   f &= g + h \
  \alpha_k &= d + \gamma_k               &   \gamma_k &=r_h - r_i   &   i &= j + k + l 
\end{align}
\kant[2][1]
\begin{flalign}
  \alpha_i &= a_ib_j - \beta_i\gamma_j   &   \gamma_i &=r_i - r_j   &   a &= b + c + d + e\
  \alpha_j &= c - \beta_j                &   \gamma_j &=r_j - r_k   &   f &= g + h \
  \alpha_k &= d + \gamma_k               &   \gamma_k &=r_h - r_i   &   i &= j + k + l 
\end{flalign}
\kant[3][1]
\par\noindent\hspace{60pt}%
\begin{minipage}{\dimexpr\textwidth-70pt} % 60pt+10pt (left+right margin)
  \begin{flalign}
    \alpha_i &= a_ib_j - \beta_i\gamma_j   &   \gamma_i &=r_i - r_j   &   a &= b + c + d + e\
    \alpha_j &= c - \beta_j                &   \gamma_j &=r_j - r_k   &   f &= g + h \
    \alpha_k &= d + \gamma_k               &   \gamma_k &=r_h - r_i   &   i &= j + k + l 
  \end{flalign}

\end{minipage}
\end{document}