2x^2+24x-432=0

Solution for 2x^2+24x-432=0 equation:

Simplifying
2x2 + 24x + -432 = 0

Reorder the terms:
-432 + 24x + 2x2 = 0

Solving
-432 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-216 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-216 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-216 + 12x + x2 = 0

Solving
-216 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + 12x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + 12x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + 12x + x2 = 0 + 216
12x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
12x + x2 = 216

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 216 + 36

Reorder the terms:
36 + 12x + x2 = 216 + 36

Combine like terms: 216 + 36 = 252
36 + 12x + x2 = 252

Factor a perfect square on the left side:
(x + 6)(x + 6) = 252

Calculate the square root of the right side: 15.874507866

Break this problem into two subproblems by setting 
(x + 6) equal to 15.874507866 and -15.874507866.

Subproblem 1
x + 6 = 15.874507866

Simplifying
x + 6 = 15.874507866

Reorder the terms:
6 + x = 15.874507866

Solving
6 + x = 15.874507866

Solving for variable 'x'.

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 = 15.874507866 + -6

Combine like terms: 6 + -6 = 0
0 + x = 15.874507866 + -6
x = 15.874507866 + -6

Combine like terms: 15.874507866 + -6 = 9.874507866
x = 9.874507866

Simplifying
x = 9.874507866

Subproblem 2
x + 6 = -15.874507866

Simplifying
x + 6 = -15.874507866

Reorder the terms:
6 + x = -15.874507866

Solving
6 + x = -15.874507866

Solving for variable 'x'.

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 = -15.874507866 + -6

Combine like terms: 6 + -6 = 0
0 + x = -15.874507866 + -6
x = -15.874507866 + -6

Combine like terms: -15.874507866 + -6 = -21.874507866
x = -21.874507866

Simplifying
x = -21.874507866

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.874507866, -21.874507866}
Solution
x = {9.874507866, -21.874507866}