Solve (2x-5)(2x+5)=left(2x-3right)^2

$$(2x-5)(2x+5)= { \left(2x-3 \right) }^{ 2 }$$

Solve for x

$$x = \frac{17}{6} = 2\frac{5}{6} \approx 2.833333333$$

Steps for Solving Linear Equation

Consider \left(2x-5\right)\left(2x+5\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 5.

$$\left(2x\right)^{2}-25=\left(2x-3\right)^{2}$$

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

$$2^{2}x^{2}-25=\left(2x-3\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-25=\left(2x-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-3\right)^{2}.

$$4x^{2}-25=4x^{2}-12x+9$$

Subtract 4x^{2} from both sides.

$$4x^{2}-25-4x^{2}=-12x+9$$

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

$$-25=-12x+9$$

Swap sides so that all variable terms are on the left hand side.

$$-12x+9=-25$$

Subtract 9 from both sides.

$$-12x=-25-9$$

Subtract 9 from -25 to get -34.

$$-12x=-34$$

Divide both sides by -12.

$$x=\frac{-34}{-12}$$

Reduce the fraction \frac{-34}{-12} to lowest terms by extracting and canceling out -2.

$$x=\frac{17}{6}$$