110=(x+6)(x+5)

Solution for 110=(x+6)(x+5) equation:

Simplifying
110 = (x + 6)(x + 5)

Reorder the terms:
110 = (6 + x)(x + 5)

Reorder the terms:
110 = (6 + x)(5 + x)

Multiply (6 + x) * (5 + x)
110 = (6(5 + x) + x(5 + x))
110 = ((5 * 6 + x * 6) + x(5 + x))
110 = ((30 + 6x) + x(5 + x))
110 = (30 + 6x + (5 * x + x * x))
110 = (30 + 6x + (5x + x2))

Combine like terms: 6x + 5x = 11x
110 = (30 + 11x + x2)

Solving
110 = 30 + 11x + x2

Solving for variable 'x'.

Combine like terms: 110 + -30 = 80
80 + -11x + -1x2 = 30 + 11x + x2 + -30 + -11x + -1x2

Reorder the terms:
80 + -11x + -1x2 = 30 + -30 + 11x + -11x + x2 + -1x2

Combine like terms: 30 + -30 = 0
80 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2
80 + -11x + -1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
80 + -11x + -1x2 = 0 + x2 + -1x2
80 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
80 + -11x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(16 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {5, -16}