x^2+7x+21=-x+6

Solution for x^2+7x+21=-x+6 equation:

Simplifying
x2 + 7x + 21 = -1x + 6

Reorder the terms:
21 + 7x + x2 = -1x + 6

Reorder the terms:
21 + 7x + x2 = 6 + -1x

Solving
21 + 7x + x2 = 6 + -1x

Solving for variable 'x'.

Reorder the terms:
21 + -6 + 7x + x + x2 = 6 + -1x + -6 + x

Combine like terms: 21 + -6 = 15
15 + 7x + x + x2 = 6 + -1x + -6 + x

Combine like terms: 7x + x = 8x
15 + 8x + x2 = 6 + -1x + -6 + x

Reorder the terms:
15 + 8x + x2 = 6 + -6 + -1x + x

Combine like terms: 6 + -6 = 0
15 + 8x + x2 = 0 + -1x + x
15 + 8x + x2 = -1x + x

Combine like terms: -1x + x = 0
15 + 8x + x2 = 0

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

Subproblem 1
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
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 = {-5, -3}