(2x-5)(2x+5)=75

Solution for (2x-5)(2x+5)=75 equation:

Simplifying
(2x + -5)(2x + 5) = 75

Reorder the terms:
(-5 + 2x)(2x + 5) = 75

Reorder the terms:
(-5 + 2x)(5 + 2x) = 75

Multiply (-5 + 2x) * (5 + 2x)
(-5(5 + 2x) + 2x * (5 + 2x)) = 75
((5 * -5 + 2x * -5) + 2x * (5 + 2x)) = 75
((-25 + -10x) + 2x * (5 + 2x)) = 75
(-25 + -10x + (5 * 2x + 2x * 2x)) = 75
(-25 + -10x + (10x + 4x2)) = 75

Combine like terms: -10x + 10x = 0
(-25 + 0 + 4x2) = 75
(-25 + 4x2) = 75

Solving
-25 + 4x2 = 75

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + 4x2 = 75 + 25

Combine like terms: -25 + 25 = 0
0 + 4x2 = 75 + 25
4x2 = 75 + 25

Combine like terms: 75 + 25 = 100
4x2 = 100

Divide each side by '4'.
x2 = 25

Simplifying
x2 = 25

Take the square root of each side:
x = {-5, 5}