(6-x)(x+6)-(x-11)x=6

Solution for (6-x)(x+6)-(x-11)x=6 equation:

Simplifying
(6 + -1x)(x + 6) + -1(x + -11) * x = 6

Reorder the terms:
(6 + -1x)(6 + x) + -1(x + -11) * x = 6

Multiply (6 + -1x) * (6 + x)
(6(6 + x) + -1x * (6 + x)) + -1(x + -11) * x = 6
((6 * 6 + x * 6) + -1x * (6 + x)) + -1(x + -11) * x = 6
((36 + 6x) + -1x * (6 + x)) + -1(x + -11) * x = 6
(36 + 6x + (6 * -1x + x * -1x)) + -1(x + -11) * x = 6
(36 + 6x + (-6x + -1x2)) + -1(x + -11) * x = 6

Combine like terms: 6x + -6x = 0
(36 + 0 + -1x2) + -1(x + -11) * x = 6
(36 + -1x2) + -1(x + -11) * x = 6

Reorder the terms:
36 + -1x2 + -1(-11 + x) * x = 6

Reorder the terms for easier multiplication:
36 + -1x2 + -1x(-11 + x) = 6
36 + -1x2 + (-11 * -1x + x * -1x) = 6
36 + -1x2 + (11x + -1x2) = 6

Reorder the terms:
36 + 11x + -1x2 + -1x2 = 6

Combine like terms: -1x2 + -1x2 = -2x2
36 + 11x + -2x2 = 6

Solving
36 + 11x + -2x2 = 6

Solving for variable 'x'.

Reorder the terms:
36 + -6 + 11x + -2x2 = 6 + -6

Combine like terms: 36 + -6 = 30
30 + 11x + -2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
30 + 11x + -2x2 = 0

Factor a trinomial.
(15 + -2x)(2 + x) = 0

Subproblem 1
Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {7.5, -2}