(x+13)13+(x+13)(x-13)1=(x-13)x

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Solution for (x+13)13+(x+13)(x-13)1=(x-13)x equation: 


Simplifying
(x + 13) * 13 + (x + 13)(x + -13) * 1 = (x + -13) * x

Reorder the terms:
(13 + x) * 13 + (x + 13)(x + -13) * 1 = (x + -13) * x

Reorder the terms for easier multiplication:
13(13 + x) + (x + 13)(x + -13) * 1 = (x + -13) * x
(13 * 13 + x * 13) + (x + 13)(x + -13) * 1 = (x + -13) * x
(169 + 13x) + (x + 13)(x + -13) * 1 = (x + -13) * x

Reorder the terms:
169 + 13x + (13 + x)(x + -13) * 1 = (x + -13) * x

Reorder the terms:
169 + 13x + (13 + x)(-13 + x) * 1 = (x + -13) * x

Reorder the terms for easier multiplication:
169 + 13x + 1(13 + x)(-13 + x) = (x + -13) * x

Multiply (13 + x) * (-13 + x)
169 + 13x + 1(13(-13 + x) + x(-13 + x)) = (x + -13) * x
169 + 13x + 1((-13 * 13 + x * 13) + x(-13 + x)) = (x + -13) * x
169 + 13x + 1((-169 + 13x) + x(-13 + x)) = (x + -13) * x
169 + 13x + 1(-169 + 13x + (-13 * x + x * x)) = (x + -13) * x
169 + 13x + 1(-169 + 13x + (-13x + x2)) = (x + -13) * x

Combine like terms: 13x + -13x = 0
169 + 13x + 1(-169 + 0 + x2) = (x + -13) * x
169 + 13x + 1(-169 + x2) = (x + -13) * x
169 + 13x + (-169 * 1 + x2 * 1) = (x + -13) * x
169 + 13x + (-169 + 1x2) = (x + -13) * x

Reorder the terms:
169 + -169 + 13x + 1x2 = (x + -13) * x

Combine like terms: 169 + -169 = 0
0 + 13x + 1x2 = (x + -13) * x
13x + 1x2 = (x + -13) * x

Reorder the terms:
13x + 1x2 = (-13 + x) * x

Reorder the terms for easier multiplication:
13x + 1x2 = x(-13 + x)
13x + 1x2 = (-13 * x + x * x)
13x + 1x2 = (-13x + x2)

Solving
13x + 1x2 = -13x + x2

Solving for variable 'x'.

Reorder the terms:
13x + 13x + 1x2 + -1x2 = -13x + x2 + 13x + -1x2

Combine like terms: 13x + 13x = 26x
26x + 1x2 + -1x2 = -13x + x2 + 13x + -1x2

Combine like terms: 1x2 + -1x2 = 0
26x + 0 = -13x + x2 + 13x + -1x2
26x = -13x + x2 + 13x + -1x2

Reorder the terms:
26x = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
26x = 0 + x2 + -1x2
26x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
26x = 0

Ignore the factor 26.

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
Solution
x = {0}

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