(2x-7)*(2x-7)-125=(3x+2)*(3x+2)

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Solution for (2x-7)*(2x-7)-125=(3x+2)*(3x+2) equation: 


Simplifying
(2x + -7)(2x + -7) + -125 = (3x + 2)(3x + 2)

Reorder the terms:
(-7 + 2x)(2x + -7) + -125 = (3x + 2)(3x + 2)

Reorder the terms:
(-7 + 2x)(-7 + 2x) + -125 = (3x + 2)(3x + 2)

Multiply (-7 + 2x) * (-7 + 2x)
(-7(-7 + 2x) + 2x * (-7 + 2x)) + -125 = (3x + 2)(3x + 2)
((-7 * -7 + 2x * -7) + 2x * (-7 + 2x)) + -125 = (3x + 2)(3x + 2)
((49 + -14x) + 2x * (-7 + 2x)) + -125 = (3x + 2)(3x + 2)
(49 + -14x + (-7 * 2x + 2x * 2x)) + -125 = (3x + 2)(3x + 2)
(49 + -14x + (-14x + 4x2)) + -125 = (3x + 2)(3x + 2)

Combine like terms: -14x + -14x = -28x
(49 + -28x + 4x2) + -125 = (3x + 2)(3x + 2)

Reorder the terms:
49 + -125 + -28x + 4x2 = (3x + 2)(3x + 2)

Combine like terms: 49 + -125 = -76
-76 + -28x + 4x2 = (3x + 2)(3x + 2)

Reorder the terms:
-76 + -28x + 4x2 = (2 + 3x)(3x + 2)

Reorder the terms:
-76 + -28x + 4x2 = (2 + 3x)(2 + 3x)

Multiply (2 + 3x) * (2 + 3x)
-76 + -28x + 4x2 = (2(2 + 3x) + 3x * (2 + 3x))
-76 + -28x + 4x2 = ((2 * 2 + 3x * 2) + 3x * (2 + 3x))
-76 + -28x + 4x2 = ((4 + 6x) + 3x * (2 + 3x))
-76 + -28x + 4x2 = (4 + 6x + (2 * 3x + 3x * 3x))
-76 + -28x + 4x2 = (4 + 6x + (6x + 9x2))

Combine like terms: 6x + 6x = 12x
-76 + -28x + 4x2 = (4 + 12x + 9x2)

Solving
-76 + -28x + 4x2 = 4 + 12x + 9x2

Solving for variable 'x'.

Reorder the terms:
-76 + -4 + -28x + -12x + 4x2 + -9x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Combine like terms: -76 + -4 = -80
-80 + -28x + -12x + 4x2 + -9x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Combine like terms: -28x + -12x = -40x
-80 + -40x + 4x2 + -9x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Combine like terms: 4x2 + -9x2 = -5x2
-80 + -40x + -5x2 = 4 + 12x + 9x2 + -4 + -12x + -9x2

Reorder the terms:
-80 + -40x + -5x2 = 4 + -4 + 12x + -12x + 9x2 + -9x2

Combine like terms: 4 + -4 = 0
-80 + -40x + -5x2 = 0 + 12x + -12x + 9x2 + -9x2
-80 + -40x + -5x2 = 12x + -12x + 9x2 + -9x2

Combine like terms: 12x + -12x = 0
-80 + -40x + -5x2 = 0 + 9x2 + -9x2
-80 + -40x + -5x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-80 + -40x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(16 + 8x + x2) = 0

Factor a trinomial.
-5((4 + x)(4 + x)) = 0

Ignore the factor -5.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

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

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