12x^2-176x-420=0

Solution for 12x^2-176x-420=0 equation:

Simplifying
12x2 + -176x + -420 = 0

Reorder the terms:
-420 + -176x + 12x2 = 0

Solving
-420 + -176x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-105 + -44x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-105 + -44x + 3x2)' equal to zero and attempt to solve:

Simplifying
-105 + -44x + 3x2 = 0

Solving
-105 + -44x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-35 + -14.66666667x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -14.66666667x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -14.66666667x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -14.66666667x + x2 = 0 + 35
-14.66666667x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-14.66666667x + x2 = 35

The x term is -14.66666667x.  Take half its coefficient (-7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
-14.66666667x + 53.77777780 + x2 = 35 + 53.77777780

Reorder the terms:
53.77777780 + -14.66666667x + x2 = 35 + 53.77777780

Combine like terms: 35 + 53.77777780 = 88.7777778
53.77777780 + -14.66666667x + x2 = 88.7777778

Factor a perfect square on the left side:
(x + -7.333333335)(x + -7.333333335) = 88.7777778

Calculate the square root of the right side: 9.422196018

Break this problem into two subproblems by setting 
(x + -7.333333335) equal to 9.422196018 and -9.422196018.

Subproblem 1
x + -7.333333335 = 9.422196018

Simplifying
x + -7.333333335 = 9.422196018

Reorder the terms:
-7.333333335 + x = 9.422196018

Solving
-7.333333335 + x = 9.422196018

Solving for variable 'x'.

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

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = 9.422196018 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = 9.422196018 + 7.333333335
x = 9.422196018 + 7.333333335

Combine like terms: 9.422196018 + 7.333333335 = 16.755529353
x = 16.755529353

Simplifying
x = 16.755529353

Subproblem 2
x + -7.333333335 = -9.422196018

Simplifying
x + -7.333333335 = -9.422196018

Reorder the terms:
-7.333333335 + x = -9.422196018

Solving
-7.333333335 + x = -9.422196018

Solving for variable 'x'.

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

Add '7.333333335' to each side of the equation.
-7.333333335 + 7.333333335 + x = -9.422196018 + 7.333333335

Combine like terms: -7.333333335 + 7.333333335 = 0.000000000
0.000000000 + x = -9.422196018 + 7.333333335
x = -9.422196018 + 7.333333335

Combine like terms: -9.422196018 + 7.333333335 = -2.088862683
x = -2.088862683

Simplifying
x = -2.088862683

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.755529353, -2.088862683}
Solution
x = {16.755529353, -2.088862683}