x^2+10x+23=-2x-4

Solution for x^2+10x+23=-2x-4 equation:

Simplifying
x2 + 10x + 23 = -2x + -4

Reorder the terms:
23 + 10x + x2 = -2x + -4

Reorder the terms:
23 + 10x + x2 = -4 + -2x

Solving
23 + 10x + x2 = -4 + -2x

Solving for variable 'x'.

Reorder the terms:
23 + 4 + 10x + 2x + x2 = -4 + -2x + 4 + 2x

Combine like terms: 23 + 4 = 27
27 + 10x + 2x + x2 = -4 + -2x + 4 + 2x

Combine like terms: 10x + 2x = 12x
27 + 12x + x2 = -4 + -2x + 4 + 2x

Reorder the terms:
27 + 12x + x2 = -4 + 4 + -2x + 2x

Combine like terms: -4 + 4 = 0
27 + 12x + x2 = 0 + -2x + 2x
27 + 12x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
27 + 12x + x2 = 0

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

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
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 = {-9, -3}