2(x+11)(x-5)-x(x+11)=72

Solution for 2(x+11)(x-5)-x(x+11)=72 equation:

Simplifying
2(x + 11)(x + -5) + -1x(x + 11) = 72

Reorder the terms:
2(11 + x)(x + -5) + -1x(x + 11) = 72

Reorder the terms:
2(11 + x)(-5 + x) + -1x(x + 11) = 72

Multiply (11 + x) * (-5 + x)
2(11(-5 + x) + x(-5 + x)) + -1x(x + 11) = 72
2((-5 * 11 + x * 11) + x(-5 + x)) + -1x(x + 11) = 72
2((-55 + 11x) + x(-5 + x)) + -1x(x + 11) = 72
2(-55 + 11x + (-5 * x + x * x)) + -1x(x + 11) = 72
2(-55 + 11x + (-5x + x2)) + -1x(x + 11) = 72

Combine like terms: 11x + -5x = 6x
2(-55 + 6x + x2) + -1x(x + 11) = 72
(-55 * 2 + 6x * 2 + x2 * 2) + -1x(x + 11) = 72
(-110 + 12x + 2x2) + -1x(x + 11) = 72

Reorder the terms:
-110 + 12x + 2x2 + -1x(11 + x) = 72
-110 + 12x + 2x2 + (11 * -1x + x * -1x) = 72
-110 + 12x + 2x2 + (-11x + -1x2) = 72

Reorder the terms:
-110 + 12x + -11x + 2x2 + -1x2 = 72

Combine like terms: 12x + -11x = 1x
-110 + 1x + 2x2 + -1x2 = 72

Combine like terms: 2x2 + -1x2 = 1x2
-110 + 1x + 1x2 = 72

Solving
-110 + 1x + 1x2 = 72

Solving for variable 'x'.

Reorder the terms:
-110 + -72 + 1x + 1x2 = 72 + -72

Combine like terms: -110 + -72 = -182
-182 + 1x + 1x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-182 + 1x + 1x2 = 0

Factor a trinomial.
(-14 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

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

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

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-14, 13}