x(11+x)=2(5x+6)

Solution for x(11+x)=2(5x+6) equation:

Simplifying
x(11 + x) = 2(5x + 6)
(11 * x + x * x) = 2(5x + 6)
(11x + x2) = 2(5x + 6)

Reorder the terms:
11x + x2 = 2(6 + 5x)
11x + x2 = (6 * 2 + 5x * 2)
11x + x2 = (12 + 10x)

Solving
11x + x2 = 12 + 10x

Solving for variable 'x'.

Reorder the terms:
-12 + 11x + -10x + x2 = 12 + 10x + -12 + -10x

Combine like terms: 11x + -10x = 1x
-12 + 1x + x2 = 12 + 10x + -12 + -10x

Reorder the terms:
-12 + 1x + x2 = 12 + -12 + 10x + -10x

Combine like terms: 12 + -12 = 0
-12 + 1x + x2 = 0 + 10x + -10x
-12 + 1x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}