(x-9)(x-9)+x^2=(x+9)(x+9)

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Solution for (x-9)(x-9)+x^2=(x+9)(x+9) equation: 


Simplifying
(x + -9)(x + -9) + x2 = (x + 9)(x + 9)

Reorder the terms:
(-9 + x)(x + -9) + x2 = (x + 9)(x + 9)

Reorder the terms:
(-9 + x)(-9 + x) + x2 = (x + 9)(x + 9)

Multiply (-9 + x) * (-9 + x)
(-9(-9 + x) + x(-9 + x)) + x2 = (x + 9)(x + 9)
((-9 * -9 + x * -9) + x(-9 + x)) + x2 = (x + 9)(x + 9)
((81 + -9x) + x(-9 + x)) + x2 = (x + 9)(x + 9)
(81 + -9x + (-9 * x + x * x)) + x2 = (x + 9)(x + 9)
(81 + -9x + (-9x + x2)) + x2 = (x + 9)(x + 9)

Combine like terms: -9x + -9x = -18x
(81 + -18x + x2) + x2 = (x + 9)(x + 9)

Combine like terms: x2 + x2 = 2x2
81 + -18x + 2x2 = (x + 9)(x + 9)

Reorder the terms:
81 + -18x + 2x2 = (9 + x)(x + 9)

Reorder the terms:
81 + -18x + 2x2 = (9 + x)(9 + x)

Multiply (9 + x) * (9 + x)
81 + -18x + 2x2 = (9(9 + x) + x(9 + x))
81 + -18x + 2x2 = ((9 * 9 + x * 9) + x(9 + x))
81 + -18x + 2x2 = ((81 + 9x) + x(9 + x))
81 + -18x + 2x2 = (81 + 9x + (9 * x + x * x))
81 + -18x + 2x2 = (81 + 9x + (9x + x2))

Combine like terms: 9x + 9x = 18x
81 + -18x + 2x2 = (81 + 18x + x2)

Add '-81' to each side of the equation.
81 + -18x + -81 + 2x2 = 81 + 18x + -81 + x2

Reorder the terms:
81 + -81 + -18x + 2x2 = 81 + 18x + -81 + x2

Combine like terms: 81 + -81 = 0
0 + -18x + 2x2 = 81 + 18x + -81 + x2
-18x + 2x2 = 81 + 18x + -81 + x2

Reorder the terms:
-18x + 2x2 = 81 + -81 + 18x + x2

Combine like terms: 81 + -81 = 0
-18x + 2x2 = 0 + 18x + x2
-18x + 2x2 = 18x + x2

Solving
-18x + 2x2 = 18x + x2

Solving for variable 'x'.

Reorder the terms:
-18x + -18x + 2x2 + -1x2 = 18x + x2 + -18x + -1x2

Combine like terms: -18x + -18x = -36x
-36x + 2x2 + -1x2 = 18x + x2 + -18x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-36x + 1x2 = 18x + x2 + -18x + -1x2

Reorder the terms:
-36x + 1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
-36x + 1x2 = 0 + x2 + -1x2
-36x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-36 + 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 '(-36 + x)' equal to zero and attempt to solve:

Simplifying
-36 + x = 0

Solving
-36 + x = 0

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

Add '36' to each side of the equation.
-36 + 36 + x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + x = 0 + 36
x = 0 + 36

Combine like terms: 0 + 36 = 36
x = 36

Simplifying
x = 36
Solution
x = {0, 36}

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