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

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


Simplifying
(x + -5)(x + -5) + x2 = (x + 5)(x + 5)

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

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

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + x2 = (x + 5)(x + 5)
((-5 * -5 + x * -5) + x(-5 + x)) + x2 = (x + 5)(x + 5)
((25 + -5x) + x(-5 + x)) + x2 = (x + 5)(x + 5)
(25 + -5x + (-5 * x + x * x)) + x2 = (x + 5)(x + 5)
(25 + -5x + (-5x + x2)) + x2 = (x + 5)(x + 5)

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

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

Reorder the terms:
25 + -10x + 2x2 = (5 + x)(x + 5)

Reorder the terms:
25 + -10x + 2x2 = (5 + x)(5 + x)

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

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

Add '-25' to each side of the equation.
25 + -10x + -25 + 2x2 = 25 + 10x + -25 + x2

Reorder the terms:
25 + -25 + -10x + 2x2 = 25 + 10x + -25 + x2

Combine like terms: 25 + -25 = 0
0 + -10x + 2x2 = 25 + 10x + -25 + x2
-10x + 2x2 = 25 + 10x + -25 + x2

Reorder the terms:
-10x + 2x2 = 25 + -25 + 10x + x2

Combine like terms: 25 + -25 = 0
-10x + 2x2 = 0 + 10x + x2
-10x + 2x2 = 10x + x2

Solving
-10x + 2x2 = 10x + x2

Solving for variable 'x'.

Reorder the terms:
-10x + -10x + 2x2 + -1x2 = 10x + x2 + -10x + -1x2

Combine like terms: -10x + -10x = -20x
-20x + 2x2 + -1x2 = 10x + x2 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-20x + 1x2 = 10x + x2 + -10x + -1x2

Reorder the terms:
-20x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-20x + 1x2 = 0 + x2 + -1x2
-20x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20
Solution
x = {0, 20}

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