x^2+15x+43=x-6

Solution for x^2+15x+43=x-6 equation:

Simplifying
x2 + 15x + 43 = x + -6

Reorder the terms:
43 + 15x + x2 = x + -6

Reorder the terms:
43 + 15x + x2 = -6 + x

Solving
43 + 15x + x2 = -6 + x

Solving for variable 'x'.

Reorder the terms:
43 + 6 + 15x + -1x + x2 = -6 + x + 6 + -1x

Combine like terms: 43 + 6 = 49
49 + 15x + -1x + x2 = -6 + x + 6 + -1x

Combine like terms: 15x + -1x = 14x
49 + 14x + x2 = -6 + x + 6 + -1x

Reorder the terms:
49 + 14x + x2 = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
49 + 14x + x2 = 0 + x + -1x
49 + 14x + x2 = x + -1x

Combine like terms: x + -1x = 0
49 + 14x + x2 = 0

Factor a trinomial.
(7 + x)(7 + 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 '(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
Solution
x = {-7, -7}