Solve 3x+2y^6=0

$$3 x + 2 y ^ { 6 } = 0$$

Solve for x

$$x=-\frac{2y^{6}}{3}$$

Steps for Solving Linear Equation

Subtract 2y^{6} from both sides. Anything subtracted from zero gives its negation.

$$3x=-2y^{6}$$

Divide both sides by 3.

$$\frac{3x}{3}=-\frac{2y^{6}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=-\frac{2y^{6}}{3}$$

Solve for y (complex solution)

$$y\in \frac{2^{\frac{5}{6}}i\sqrt[6]{3x}}{2},\frac{2^{\frac{5}{6}}e^{\frac{\pi i}{6}}\sqrt[6]{3x}}{2},\frac{2^{\frac{5}{6}}e^{\frac{5\pi i}{6}}\sqrt[6]{3x}}{2},\frac{2^{\frac{5}{6}}e^{\frac{7\pi i}{6}}\sqrt[6]{3x}}{2},-\frac{2^{\frac{5}{6}}i\sqrt[6]{3x}}{2},\frac{2^{\frac{5}{6}}e^{\frac{11\pi i}{6}}\sqrt[6]{3x}}{2}$$

Solve for y

$$y=\frac{2^{\frac{5}{6}}\sqrt[6]{-3x}}{2}$$

$$y=-\frac{2^{\frac{5}{6}}\sqrt[6]{-3x}}{2}\text{, }x\leq 0$$