112=(x+4)(2x+6)

Solution for 112=(x+4)(2x+6) equation:

Simplifying
112 = (x + 4)(2x + 6)

Reorder the terms:
112 = (4 + x)(2x + 6)

Reorder the terms:
112 = (4 + x)(6 + 2x)

Multiply (4 + x) * (6 + 2x)
112 = (4(6 + 2x) + x(6 + 2x))
112 = ((6 * 4 + 2x * 4) + x(6 + 2x))
112 = ((24 + 8x) + x(6 + 2x))
112 = (24 + 8x + (6 * x + 2x * x))
112 = (24 + 8x + (6x + 2x2))

Combine like terms: 8x + 6x = 14x
112 = (24 + 14x + 2x2)

Solving
112 = 24 + 14x + 2x2

Solving for variable 'x'.

Combine like terms: 112 + -24 = 88
88 + -14x + -2x2 = 24 + 14x + 2x2 + -24 + -14x + -2x2

Reorder the terms:
88 + -14x + -2x2 = 24 + -24 + 14x + -14x + 2x2 + -2x2

Combine like terms: 24 + -24 = 0
88 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2
88 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
88 + -14x + -2x2 = 0 + 2x2 + -2x2
88 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
88 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(44 + -7x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(11 + x)) = 0

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

Simplifying
11 + x = 0

Solving
11 + x = 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 + x = 0 + -11

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

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

Simplifying
x = -11
Solution
x = {4, -11}