Solve q=2/27a^3-ab/3+c

$$q = \frac { 2 } { 27 } a ^ { 3 } - \frac { a b } { 3 } + c$$

Solve for b

$$\left\{\begin{matrix}b=\frac{27c+2a^{3}-27q}{9a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&q=c\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{2}{27}a^{3}-\frac{ab}{3}+c=q$$

Subtract \frac{2}{27}a^{3} from both sides.

$$-\frac{ab}{3}+c=q-\frac{2}{27}a^{3}$$

Subtract c from both sides.

$$-\frac{ab}{3}=q-\frac{2}{27}a^{3}-c$$

Multiply both sides of the equation by 27, the least common multiple of 3,27.

$$-9ab=27q-2a^{3}-27c$$

The equation is in standard form.

$$\left(-9a\right)b=27q-2a^{3}-27c$$

Divide both sides by -9a.

$$\frac{\left(-9a\right)b}{-9a}=\frac{27q-2a^{3}-27c}{-9a}$$

Dividing by -9a undoes the multiplication by -9a.

$$b=\frac{27q-2a^{3}-27c}{-9a}$$

Divide 27q-2a^{3}-27c by -9a.

$$b=-\frac{27q-2a^{3}-27c}{9a}$$