(x-6)(x-6)+(x+8)(x+8)=(2x-26)(2x-26)

Solution for (x-6)(x-6)+(x+8)(x+8)=(2x-26)(2x-26) equation:

Simplifying
(x + -6)(x + -6) + (x + 8)(x + 8) = (2x + -26)(2x + -26)

Reorder the terms:
(-6 + x)(x + -6) + (x + 8)(x + 8) = (2x + -26)(2x + -26)

Reorder the terms:
(-6 + x)(-6 + x) + (x + 8)(x + 8) = (2x + -26)(2x + -26)

Multiply (-6 + x) * (-6 + x)
(-6(-6 + x) + x(-6 + x)) + (x + 8)(x + 8) = (2x + -26)(2x + -26)
((-6 * -6 + x * -6) + x(-6 + x)) + (x + 8)(x + 8) = (2x + -26)(2x + -26)
((36 + -6x) + x(-6 + x)) + (x + 8)(x + 8) = (2x + -26)(2x + -26)
(36 + -6x + (-6 * x + x * x)) + (x + 8)(x + 8) = (2x + -26)(2x + -26)
(36 + -6x + (-6x + x2)) + (x + 8)(x + 8) = (2x + -26)(2x + -26)

Combine like terms: -6x + -6x = -12x
(36 + -12x + x2) + (x + 8)(x + 8) = (2x + -26)(2x + -26)

Reorder the terms:
36 + -12x + x2 + (8 + x)(x + 8) = (2x + -26)(2x + -26)

Reorder the terms:
36 + -12x + x2 + (8 + x)(8 + x) = (2x + -26)(2x + -26)

Multiply (8 + x) * (8 + x)
36 + -12x + x2 + (8(8 + x) + x(8 + x)) = (2x + -26)(2x + -26)
36 + -12x + x2 + ((8 * 8 + x * 8) + x(8 + x)) = (2x + -26)(2x + -26)
36 + -12x + x2 + ((64 + 8x) + x(8 + x)) = (2x + -26)(2x + -26)
36 + -12x + x2 + (64 + 8x + (8 * x + x * x)) = (2x + -26)(2x + -26)
36 + -12x + x2 + (64 + 8x + (8x + x2)) = (2x + -26)(2x + -26)

Combine like terms: 8x + 8x = 16x
36 + -12x + x2 + (64 + 16x + x2) = (2x + -26)(2x + -26)

Reorder the terms:
36 + 64 + -12x + 16x + x2 + x2 = (2x + -26)(2x + -26)

Combine like terms: 36 + 64 = 100
100 + -12x + 16x + x2 + x2 = (2x + -26)(2x + -26)

Combine like terms: -12x + 16x = 4x
100 + 4x + x2 + x2 = (2x + -26)(2x + -26)

Combine like terms: x2 + x2 = 2x2
100 + 4x + 2x2 = (2x + -26)(2x + -26)

Reorder the terms:
100 + 4x + 2x2 = (-26 + 2x)(2x + -26)

Reorder the terms:
100 + 4x + 2x2 = (-26 + 2x)(-26 + 2x)

Multiply (-26 + 2x) * (-26 + 2x)
100 + 4x + 2x2 = (-26(-26 + 2x) + 2x * (-26 + 2x))
100 + 4x + 2x2 = ((-26 * -26 + 2x * -26) + 2x * (-26 + 2x))
100 + 4x + 2x2 = ((676 + -52x) + 2x * (-26 + 2x))
100 + 4x + 2x2 = (676 + -52x + (-26 * 2x + 2x * 2x))
100 + 4x + 2x2 = (676 + -52x + (-52x + 4x2))

Combine like terms: -52x + -52x = -104x
100 + 4x + 2x2 = (676 + -104x + 4x2)

Solving
100 + 4x + 2x2 = 676 + -104x + 4x2

Solving for variable 'x'.

Reorder the terms:
100 + -676 + 4x + 104x + 2x2 + -4x2 = 676 + -104x + 4x2 + -676 + 104x + -4x2

Combine like terms: 100 + -676 = -576
-576 + 4x + 104x + 2x2 + -4x2 = 676 + -104x + 4x2 + -676 + 104x + -4x2

Combine like terms: 4x + 104x = 108x
-576 + 108x + 2x2 + -4x2 = 676 + -104x + 4x2 + -676 + 104x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-576 + 108x + -2x2 = 676 + -104x + 4x2 + -676 + 104x + -4x2

Reorder the terms:
-576 + 108x + -2x2 = 676 + -676 + -104x + 104x + 4x2 + -4x2

Combine like terms: 676 + -676 = 0
-576 + 108x + -2x2 = 0 + -104x + 104x + 4x2 + -4x2
-576 + 108x + -2x2 = -104x + 104x + 4x2 + -4x2

Combine like terms: -104x + 104x = 0
-576 + 108x + -2x2 = 0 + 4x2 + -4x2
-576 + 108x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-576 + 108x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-288 + 54x + -1x2) = 0

Factor a trinomial.
2((-48 + x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-48 + x)' equal to zero and attempt to solve:

Simplifying
-48 + x = 0

Solving
-48 + x = 0

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

Add '48' to each side of the equation.
-48 + 48 + x = 0 + 48

Combine like terms: -48 + 48 = 0
0 + x = 0 + 48
x = 0 + 48

Combine like terms: 0 + 48 = 48
x = 48

Simplifying
x = 48
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {48, 6}