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

$$( 2 x - 1 ) ^ { 2 } = ( 2 x + 3 ) ( 2 x - 3 )$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

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

Consider \left(2x+3\right)\left(2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-4x+1=\left(2x\right)^{2}-9$$

Expand \left(2x\right)^{2}.

$$4x^{2}-4x+1=2^{2}x^{2}-9$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-4x+1=4x^{2}-9$$

Subtract 4x^{2} from both sides.

$$4x^{2}-4x+1-4x^{2}=-9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-4x+1=-9$$

Subtract 1 from both sides.

$$-4x=-9-1$$

Subtract 1 from -9 to get -10.

$$-4x=-10$$

Divide both sides by -4.

$$x=\frac{-10}{-4}$$

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{2}$$