Multiline Equations with Explicit Labels

Simple equation

\begin{eqnarray} 32 - 9 x^3 + 20 &=& 3 - 1 \\ 9 - 27 + 20 &=& 2 \\ 9 - 7 &=& 2 \\ 2 &=& 2 \end{eqnarray}

Inequality simplification

\begin{align*} 2k+1& \geq 2k+2 \tag{Step 1}\\ & \geq 2k+2 \tag{Step 2}\\ & =2(k+1) \tag{Step 3} \end{align*}

Quadratic simplification

\begin{align*} 0.15x & = 2 + 0.12x - 0.002x^2 \\ \tag*{Bring terms to left} 0.002x^2 + 0.15x - 0.12x - 2 & = 0\\ \tag*{Simplify} 0.002x^2 + 0.03x - 2 &= 0\\ \tag*{Multiply by 500} x^2 + 15x - 1000 & = 0\\ \tag*{Split 15x} x^2 -25x + 40x - 1000 & = 0\\ \tag*{} x(x-25) + 40(x-25) & = 0\\ \tag*{} (x+40)(x-25) & = 0\\ x & = -40 \mbox{ or } 25\\ \end{align*}