4x^2=-20-24x

Solution for 4x^2=-20-24x equation:

Simplifying
4x2 = -20 + -24x

Solving
4x2 = -20 + -24x

Solving for variable 'x'.

Reorder the terms:
20 + 24x + 4x2 = -20 + -24x + 20 + 24x

Reorder the terms:
20 + 24x + 4x2 = -20 + 20 + -24x + 24x

Combine like terms: -20 + 20 = 0
20 + 24x + 4x2 = 0 + -24x + 24x
20 + 24x + 4x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
20 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 6x + x2) = 0

Factor a trinomial.
4((5 + x)(1 + x)) = 0

Ignore the factor 4.
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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-5, -1}