(2x-5)(2x-5)-x^2=32

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Solution for (2x-5)(2x-5)-x^2=32 equation: 


Simplifying
(2x + -5)(2x + -5) + -1x2 = 32

Reorder the terms:
(-5 + 2x)(2x + -5) + -1x2 = 32

Reorder the terms:
(-5 + 2x)(-5 + 2x) + -1x2 = 32

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) + -1x2 = 32
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -1x2 = 32
((25 + -10x) + 2x * (-5 + 2x)) + -1x2 = 32
(25 + -10x + (-5 * 2x + 2x * 2x)) + -1x2 = 32
(25 + -10x + (-10x + 4x2)) + -1x2 = 32

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) + -1x2 = 32

Combine like terms: 4x2 + -1x2 = 3x2
25 + -20x + 3x2 = 32

Solving
25 + -20x + 3x2 = 32

Solving for variable 'x'.

Reorder the terms:
25 + -32 + -20x + 3x2 = 32 + -32

Combine like terms: 25 + -32 = -7
-7 + -20x + 3x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-7 + -20x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(7 + -1x) = 0


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-0.3333333333, 7}

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