(2x-3)(2x-3)=25

Solution for (2x-3)(2x-3)=25 equation:

Simplifying
(2x + -3)(2x + -3) = 25

Reorder the terms:
(-3 + 2x)(2x + -3) = 25

Reorder the terms:
(-3 + 2x)(-3 + 2x) = 25

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) = 25
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 25
((9 + -6x) + 2x * (-3 + 2x)) = 25
(9 + -6x + (-3 * 2x + 2x * 2x)) = 25
(9 + -6x + (-6x + 4x2)) = 25

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) = 25

Solving
9 + -12x + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
9 + -25 + -12x + 4x2 = 25 + -25

Combine like terms: 9 + -25 = -16
-16 + -12x + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-16 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -3x + x2) = 0

Factor a trinomial.
4((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}