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

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by x-3 and combine like terms.

$$x^{2}-4x+3=\left(x+1\right)\left(x+3\right)$$

Use the distributive property to multiply x+1 by x+3 and combine like terms.

$$x^{2}-4x+3=x^{2}+4x+3$$

Subtract x^{2} from both sides.

$$x^{2}-4x+3-x^{2}=4x+3$$

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

$$-4x+3=4x+3$$

Subtract 4x from both sides.

$$-4x+3-4x=3$$

Combine -4x and -4x to get -8x.

$$-8x+3=3$$

Subtract 3 from both sides.

$$-8x=3-3$$

Subtract 3 from 3 to get 0.

$$-8x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -8 is not equal to 0, x must be equal to 0.

$$x=0$$