Solve x(x-1)-x(x-3)=12

$$x(x-1)-x(x-3)=12$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by x-1.

$$x^{2}-x-x\left(x-3\right)=12$$

Use the distributive property to multiply x by x-3.

$$x^{2}-x-\left(x^{2}-3x\right)=12$$

To find the opposite of x^{2}-3x, find the opposite of each term.

$$x^{2}-x-x^{2}-\left(-3x\right)=12$$

The opposite of -3x is 3x.

$$x^{2}-x-x^{2}+3x=12$$

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

$$-x+3x=12$$

Combine -x and 3x to get 2x.

$$2x=12$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x=6$$