4x^2+72x-576=0

Solution for 4x^2+72x-576=0 equation:

Simplifying
4x2 + 72x + -576 = 0

Reorder the terms:
-576 + 72x + 4x2 = 0

Solving
-576 + 72x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-144 + 18x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-24, 6}