Solve (x+d)(x+2d)-x(x+d)=18

$$( x + d ) ( x + 2 d ) - x ( x + d ) = 18$$

Solve for x

$$x=-d+\frac{9}{d}$$

$$d\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+d by x+2d and combine like terms.

$$x^{2}+3xd+2d^{2}-x\left(x+d\right)=18$$

Use the distributive property to multiply x by x+d.

$$x^{2}+3xd+2d^{2}-\left(x^{2}+xd\right)=18$$

To find the opposite of x^{2}+xd, find the opposite of each term.

$$x^{2}+3xd+2d^{2}-x^{2}-xd=18$$

Combine x^{2} and -x^{2} to get 0.

$$3xd+2d^{2}-xd=18$$

Combine 3xd and -xd to get 2xd.

$$2xd+2d^{2}=18$$

Subtract 2d^{2} from both sides.

$$2xd=18-2d^{2}$$

The equation is in standard form.

$$2dx=18-2d^{2}$$

Divide both sides by 2d.

$$\frac{2dx}{2d}=\frac{18-2d^{2}}{2d}$$

Dividing by 2d undoes the multiplication by 2d.

$$x=\frac{18-2d^{2}}{2d}$$

Divide -2d^{2}+18 by 2d.

$$x=-d+\frac{9}{d}$$

Solve for d

$$d=\frac{\sqrt{x^{2}+36}-x}{2}$$

$$d=\frac{-\sqrt{x^{2}+36}-x}{2}$$