x^2+12x+48=-x+6

Solution for x^2+12x+48=-x+6 equation:

Simplifying
x2 + 12x + 48 = -1x + 6

Reorder the terms:
48 + 12x + x2 = -1x + 6

Reorder the terms:
48 + 12x + x2 = 6 + -1x

Solving
48 + 12x + x2 = 6 + -1x

Solving for variable 'x'.

Reorder the terms:
48 + -6 + 12x + x + x2 = 6 + -1x + -6 + x

Combine like terms: 48 + -6 = 42
42 + 12x + x + x2 = 6 + -1x + -6 + x

Combine like terms: 12x + x = 13x
42 + 13x + x2 = 6 + -1x + -6 + x

Reorder the terms:
42 + 13x + x2 = 6 + -6 + -1x + x

Combine like terms: 6 + -6 = 0
42 + 13x + x2 = 0 + -1x + x
42 + 13x + x2 = -1x + x

Combine like terms: -1x + x = 0
42 + 13x + x2 = 0

Factor a trinomial.
(7 + x)(6 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-7, -6}