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

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


Simplifying
(x + -5)(x + -5) + -1(2x)(2x) = 0

Reorder the terms:
(-5 + x)(x + -5) + -1(2x)(2x) = 0

Reorder the terms:
(-5 + x)(-5 + x) + -1(2x)(2x) = 0

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -1(2x)(2x) = 0
((-5 * -5 + x * -5) + x(-5 + x)) + -1(2x)(2x) = 0
((25 + -5x) + x(-5 + x)) + -1(2x)(2x) = 0
(25 + -5x + (-5 * x + x * x)) + -1(2x)(2x) = 0
(25 + -5x + (-5x + x2)) + -1(2x)(2x) = 0

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -1(2x)(2x) = 0

Remove parenthesis around (2x)
25 + -10x + x2 + -1 * 2x(2x) = 0

Remove parenthesis around (2x)
25 + -10x + x2 + -1 * 2x * 2x = 0

Reorder the terms for easier multiplication:
25 + -10x + x2 + -1 * 2 * 2x * x = 0

Multiply -1 * 2
25 + -10x + x2 + -2 * 2x * x = 0

Multiply -2 * 2
25 + -10x + x2 + -4x * x = 0

Multiply x * x
25 + -10x + x2 + -4x2 = 0

Combine like terms: x2 + -4x2 = -3x2
25 + -10x + -3x2 = 0

Solving
25 + -10x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -3x)(5 + x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {1.666666667, -5}

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