7=(x+6)(x+12)

Solution for 7=(x+6)(x+12) equation:

Simplifying
7 = (x + 6)(x + 12)

Reorder the terms:
7 = (6 + x)(x + 12)

Reorder the terms:
7 = (6 + x)(12 + x)

Multiply (6 + x) * (12 + x)
7 = (6(12 + x) + x(12 + x))
7 = ((12 * 6 + x * 6) + x(12 + x))
7 = ((72 + 6x) + x(12 + x))
7 = (72 + 6x + (12 * x + x * x))
7 = (72 + 6x + (12x + x2))

Combine like terms: 6x + 12x = 18x
7 = (72 + 18x + x2)

Solving
7 = 72 + 18x + x2

Solving for variable 'x'.

Combine like terms: 7 + -72 = -65
-65 + -18x + -1x2 = 72 + 18x + x2 + -72 + -18x + -1x2

Reorder the terms:
-65 + -18x + -1x2 = 72 + -72 + 18x + -18x + x2 + -1x2

Combine like terms: 72 + -72 = 0
-65 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2
-65 + -18x + -1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
-65 + -18x + -1x2 = 0 + x2 + -1x2
-65 + -18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-65 + -18x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(65 + 18x + x2) = 0

Factor a trinomial.
-1((13 + x)(5 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 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 + x = 0 + -13

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

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

Simplifying
x = -13
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-13, -5}