(2x-1)(2x-1)-25=0

Solution for (2x-1)(2x-1)-25=0 equation:

Simplifying
(2x + -1)(2x + -1) + -25 = 0

Reorder the terms:
(-1 + 2x)(2x + -1) + -25 = 0

Reorder the terms:
(-1 + 2x)(-1 + 2x) + -25 = 0

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) + -25 = 0
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -25 = 0
((1 + -2x) + 2x * (-1 + 2x)) + -25 = 0
(1 + -2x + (-1 * 2x + 2x * 2x)) + -25 = 0
(1 + -2x + (-2x + 4x2)) + -25 = 0

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) + -25 = 0

Reorder the terms:
1 + -25 + -4x + 4x2 = 0

Combine like terms: 1 + -25 = -24
-24 + -4x + 4x2 = 0

Solving
-24 + -4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(3 + -1x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}