Solve (2x-1)(x-3)=(2x-3)(x-1)

$$( 2 x - 1 ) ( x - 3 ) = ( 2 x - 3 ) ( x - 1 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by x-3 and combine like terms.

$$2x^{2}-7x+3=\left(2x-3\right)\left(x-1\right)$$

Use the distributive property to multiply 2x-3 by x-1 and combine like terms.

$$2x^{2}-7x+3=2x^{2}-5x+3$$

Subtract 2x^{2} from both sides.

$$2x^{2}-7x+3-2x^{2}=-5x+3$$

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

$$-7x+3=-5x+3$$

Add 5x to both sides.

$$-7x+3+5x=3$$

Combine -7x and 5x to get -2x.

$$-2x+3=3$$

Subtract 3 from both sides.

$$-2x=3-3$$

Subtract 3 from 3 to get 0.

$$-2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.

$$x=0$$