x^2+10x+4=-20

Solution for x^2+10x+4=-20 equation:

Simplifying
x2 + 10x + 4 = -20

Reorder the terms:
4 + 10x + x2 = -20

Solving
4 + 10x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
4 + 20 + 10x + x2 = -20 + 20

Combine like terms: 4 + 20 = 24
24 + 10x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
24 + 10x + x2 = 0

Factor a trinomial.
(6 + x)(4 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-6, -4}