(x-1)(x-1)+(x+6)(x+6)=(13)(13)

Solution for (x-1)(x-1)+(x+6)(x+6)=(13)(13) equation:

Simplifying
(x + -1)(x + -1) + (x + 6)(x + 6) = (13)(13)

Reorder the terms:
(-1 + x)(x + -1) + (x + 6)(x + 6) = (13)(13)

Reorder the terms:
(-1 + x)(-1 + x) + (x + 6)(x + 6) = (13)(13)

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) + (x + 6)(x + 6) = (13)(13)
((-1 * -1 + x * -1) + x(-1 + x)) + (x + 6)(x + 6) = (13)(13)
((1 + -1x) + x(-1 + x)) + (x + 6)(x + 6) = (13)(13)
(1 + -1x + (-1 * x + x * x)) + (x + 6)(x + 6) = (13)(13)
(1 + -1x + (-1x + x2)) + (x + 6)(x + 6) = (13)(13)

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) + (x + 6)(x + 6) = (13)(13)

Reorder the terms:
1 + -2x + x2 + (6 + x)(x + 6) = (13)(13)

Reorder the terms:
1 + -2x + x2 + (6 + x)(6 + x) = (13)(13)

Multiply (6 + x) * (6 + x)
1 + -2x + x2 + (6(6 + x) + x(6 + x)) = (13)(13)
1 + -2x + x2 + ((6 * 6 + x * 6) + x(6 + x)) = (13)(13)
1 + -2x + x2 + ((36 + 6x) + x(6 + x)) = (13)(13)
1 + -2x + x2 + (36 + 6x + (6 * x + x * x)) = (13)(13)
1 + -2x + x2 + (36 + 6x + (6x + x2)) = (13)(13)

Combine like terms: 6x + 6x = 12x
1 + -2x + x2 + (36 + 12x + x2) = (13)(13)

Reorder the terms:
1 + 36 + -2x + 12x + x2 + x2 = (13)(13)

Combine like terms: 1 + 36 = 37
37 + -2x + 12x + x2 + x2 = (13)(13)

Combine like terms: -2x + 12x = 10x
37 + 10x + x2 + x2 = (13)(13)

Combine like terms: x2 + x2 = 2x2
37 + 10x + 2x2 = (13)(13)

Multiply 13 * 13
37 + 10x + 2x2 = 169

Solving
37 + 10x + 2x2 = 169

Solving for variable 'x'.

Reorder the terms:
37 + -169 + 10x + 2x2 = 169 + -169

Combine like terms: 37 + -169 = -132
-132 + 10x + 2x2 = 169 + -169

Combine like terms: 169 + -169 = 0
-132 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + 5x + x2) = 0

Factor a trinomial.
2((-11 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
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 = {-11, 6}