(2x-5)(2x-5)-121=0

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Solution for (2x-5)(2x-5)-121=0 equation: 


Simplifying
(2x + -5)(2x + -5) + -121 = 0

Reorder the terms:
(-5 + 2x)(2x + -5) + -121 = 0

Reorder the terms:
(-5 + 2x)(-5 + 2x) + -121 = 0

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) + -121 = 0
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -121 = 0
((25 + -10x) + 2x * (-5 + 2x)) + -121 = 0
(25 + -10x + (-5 * 2x + 2x * 2x)) + -121 = 0
(25 + -10x + (-10x + 4x2)) + -121 = 0

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) + -121 = 0

Reorder the terms:
25 + -121 + -20x + 4x2 = 0

Combine like terms: 25 + -121 = -96
-96 + -20x + 4x2 = 0

Solving
-96 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -5x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}

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