Solve z*(x+1)-sqrt[3]{32}=x-20

$$z \cdot ( x + 1 ) - \sqrt[ 3 ] { 32 } = x - 20$$

Solve for x

$$x=-\frac{z+20-2\sqrt[3]{4}}{z-1}$$

$$z\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by x+1.

$$zx+z-\sqrt[3]{32}=x-20$$

Subtract x from both sides.

$$zx+z-\sqrt[3]{32}-x=-20$$

Subtract z from both sides.

$$zx-\sqrt[3]{32}-x=-20-z$$

Add \sqrt[3]{32} to both sides.

$$zx-x=-20-z+\sqrt[3]{32}$$

Combine all terms containing x.

$$\left(z-1\right)x=-20-z+\sqrt[3]{32}$$

The equation is in standard form.

$$\left(z-1\right)x=-z+\sqrt[3]{32}-20$$

Divide both sides by z-1.

$$\frac{\left(z-1\right)x}{z-1}=\frac{-z+2\times 2^{\frac{2}{3}}-20}{z-1}$$

Dividing by z-1 undoes the multiplication by z-1.

$$x=\frac{-z+2\times 2^{\frac{2}{3}}-20}{z-1}$$

Solve for z

$$z=-\frac{-x+20-2\sqrt[3]{4}}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by x+1.

$$zx+z-\sqrt[3]{32}=x-20$$

Add \sqrt[3]{32} to both sides.

$$zx+z=x-20+\sqrt[3]{32}$$

Combine all terms containing z.

$$\left(x+1\right)z=x-20+\sqrt[3]{32}$$

The equation is in standard form.

$$\left(x+1\right)z=x+\sqrt[3]{32}-20$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)z}{x+1}=\frac{x+2\times 2^{\frac{2}{3}}-20}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$z=\frac{x+2\times 2^{\frac{2}{3}}-20}{x+1}$$