-12x^2+4x+400=0

Solution for -12x^2+4x+400=0 equation:

Simplifying
-12x2 + 4x + 400 = 0

Reorder the terms:
400 + 4x + -12x2 = 0

Solving
400 + 4x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(100 + x + -3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(100 + x + -3x2)' equal to zero and attempt to solve:

Simplifying
100 + x + -3x2 = 0

Solving
100 + x + -3x2 = 0

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

Divide each side by '-3'.
-33.33333333 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + -0.3333333333x + 33.33333333 + x2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + -0.3333333333x + x2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + -0.3333333333x + x2 = 0 + 33.33333333
-0.3333333333x + x2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
-0.3333333333x + x2 = 33.33333333

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333x + 0.25 + x2 = 33.33333333 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = 33.33333333 + 0.25

Combine like terms: 33.33333333 + 0.25 = 33.58333333
0.25 + -0.3333333333x + x2 = 33.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 33.58333333

Calculate the square root of the right side: 5.795112883

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.795112883 and -5.795112883.

Subproblem 1
x + 0.5 = 5.795112883

Simplifying
x + 0.5 = 5.795112883

Reorder the terms:
0.5 + x = 5.795112883

Solving
0.5 + x = 5.795112883

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.795112883 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.795112883 + -0.5
x = 5.795112883 + -0.5

Combine like terms: 5.795112883 + -0.5 = 5.295112883
x = 5.295112883

Simplifying
x = 5.295112883

Subproblem 2
x + 0.5 = -5.795112883

Simplifying
x + 0.5 = -5.795112883

Reorder the terms:
0.5 + x = -5.795112883

Solving
0.5 + x = -5.795112883

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.795112883 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.795112883 + -0.5
x = -5.795112883 + -0.5

Combine like terms: -5.795112883 + -0.5 = -6.295112883
x = -6.295112883

Simplifying
x = -6.295112883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.295112883, -6.295112883}
Solution
x = {5.295112883, -6.295112883}