Solve 8x^3+12y=0

$$8 x ^ { 3 } + 12 y = 0$$

Solve for y

$$y=-\frac{2x^{3}}{3}$$

Steps for Solving Linear Equation

Subtract 8x^{3} from both sides. Anything subtracted from zero gives its negation.

$$12y=-8x^{3}$$

Divide both sides by 12.

$$\frac{12y}{12}=-\frac{8x^{3}}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$y=-\frac{8x^{3}}{12}$$

Divide -8x^{3} by 12.

$$y=-\frac{2x^{3}}{3}$$

Solve for x (complex solution)

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{3y}}{2}$$

$$x=\frac{2^{\frac{2}{3}}e^{\frac{\pi i}{3}}\sqrt[3]{3y}}{2}$$

$$x=\frac{2^{\frac{2}{3}}e^{\frac{5\pi i}{3}}\sqrt[3]{3y}}{2}$$

Solve for x

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{3y}}{2}$$