(x^2-8x+16)+(x^2-16x+64)=x^2

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Solution for (x^2-8x+16)+(x^2-16x+64)=x^2 equation: 


Simplifying
(x2 + -8x + 16) + (x2 + -16x + 64) = x2

Reorder the terms:
(16 + -8x + x2) + (x2 + -16x + 64) = x2

Remove parenthesis around (16 + -8x + x2)
16 + -8x + x2 + (x2 + -16x + 64) = x2

Reorder the terms:
16 + -8x + x2 + (64 + -16x + x2) = x2

Remove parenthesis around (64 + -16x + x2)
16 + -8x + x2 + 64 + -16x + x2 = x2

Reorder the terms:
16 + 64 + -8x + -16x + x2 + x2 = x2

Combine like terms: 16 + 64 = 80
80 + -8x + -16x + x2 + x2 = x2

Combine like terms: -8x + -16x = -24x
80 + -24x + x2 + x2 = x2

Combine like terms: x2 + x2 = 2x2
80 + -24x + 2x2 = x2

Solving
80 + -24x + 2x2 = x2

Solving for variable 'x'.

Combine like terms: 2x2 + -1x2 = 1x2
80 + -24x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -24x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(20 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 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 + -1x = 0 + -20

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

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

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {4, 20}

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