4x^2+56x-396=0

Solution for 4x^2+56x-396=0 equation:

Simplifying
4x2 + 56x + -396 = 0

Reorder the terms:
-396 + 56x + 4x2 = 0

Solving
-396 + 56x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-99 + 14x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-99 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-99 + 14x + x2 = 0

Solving
-99 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '99' to each side of the equation.
-99 + 14x + 99 + x2 = 0 + 99

Reorder the terms:
-99 + 99 + 14x + x2 = 0 + 99

Combine like terms: -99 + 99 = 0
0 + 14x + x2 = 0 + 99
14x + x2 = 0 + 99

Combine like terms: 0 + 99 = 99
14x + x2 = 99

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 99 + 49

Reorder the terms:
49 + 14x + x2 = 99 + 49

Combine like terms: 99 + 49 = 148
49 + 14x + x2 = 148

Factor a perfect square on the left side:
(x + 7)(x + 7) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(x + 7) equal to 12.165525061 and -12.165525061.

Subproblem 1
x + 7 = 12.165525061

Simplifying
x + 7 = 12.165525061

Reorder the terms:
7 + x = 12.165525061

Solving
7 + x = 12.165525061

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 12.165525061 + -7

Combine like terms: 7 + -7 = 0
0 + x = 12.165525061 + -7
x = 12.165525061 + -7

Combine like terms: 12.165525061 + -7 = 5.165525061
x = 5.165525061

Simplifying
x = 5.165525061

Subproblem 2
x + 7 = -12.165525061

Simplifying
x + 7 = -12.165525061

Reorder the terms:
7 + x = -12.165525061

Solving
7 + x = -12.165525061

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -12.165525061 + -7

Combine like terms: 7 + -7 = 0
0 + x = -12.165525061 + -7
x = -12.165525061 + -7

Combine like terms: -12.165525061 + -7 = -19.165525061
x = -19.165525061

Simplifying
x = -19.165525061

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.165525061, -19.165525061}
Solution
x = {5.165525061, -19.165525061}