Solve -2/4x=16w^3

$$\frac { - 2 } { 4 x } = 16 w ^ { 3 }$$

Solve for x

$$x=-\frac{1}{32w^{3}}$$

$$w\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x.

$$-2=16w^{3}\times 4x$$

Multiply 16 and 4 to get 64.

$$-2=64w^{3}x$$

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

$$64w^{3}x=-2$$

Divide both sides by 64w^{3}.

$$\frac{64w^{3}x}{64w^{3}}=-\frac{2}{64w^{3}}$$

Dividing by 64w^{3} undoes the multiplication by 64w^{3}.

$$x=-\frac{2}{64w^{3}}$$

Divide -2 by 64w^{3}.

$$x=-\frac{1}{32w^{3}}$$

Variable x cannot be equal to 0.

$$x=-\frac{1}{32w^{3}}\text{, }x\neq 0$$

Solve for w (complex solution)

$$w=-\frac{4^{\frac{2}{3}}x^{-\frac{1}{3}}}{8}$$

$$w=\frac{\sqrt[3]{2}e^{\frac{\pi i}{3}}x^{-\frac{1}{3}}}{4}$$

$$w=\frac{\sqrt[3]{2}e^{\frac{5\pi i}{3}}x^{-\frac{1}{3}}}{4}\text{, }x\neq 0$$

Solve for w

$$w=-\frac{4^{\frac{2}{3}}}{8\sqrt[3]{x}}$$

$$x\neq 0$$