x^2+7x+15=x+6

Solution for x^2+7x+15=x+6 equation:

Simplifying
x2 + 7x + 15 = x + 6

Reorder the terms:
15 + 7x + x2 = x + 6

Reorder the terms:
15 + 7x + x2 = 6 + x

Solving
15 + 7x + x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
15 + -6 + 7x + -1x + x2 = 6 + x + -6 + -1x

Combine like terms: 15 + -6 = 9
9 + 7x + -1x + x2 = 6 + x + -6 + -1x

Combine like terms: 7x + -1x = 6x
9 + 6x + x2 = 6 + x + -6 + -1x

Reorder the terms:
9 + 6x + x2 = 6 + -6 + x + -1x

Combine like terms: 6 + -6 = 0
9 + 6x + x2 = 0 + x + -1x
9 + 6x + x2 = x + -1x

Combine like terms: x + -1x = 0
9 + 6x + x2 = 0

Factor a trinomial.
(3 + x)(3 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-3, -3}