12x^2+48x-4=0

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Solution for 12x^2+48x-4=0 equation: 


Simplifying
12x2 + 48x + -4 = 0

Reorder the terms:
-4 + 48x + 12x2 = 0

Solving
-4 + 48x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 12x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + 3x2 = 0

Solving
-1 + 12x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 4x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 4x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 4x + x2 = 0 + 0.3333333333
4x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
4x + x2 = 0.3333333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 0.3333333333 + 4

Reorder the terms:
4 + 4x + x2 = 0.3333333333 + 4

Combine like terms: 0.3333333333 + 4 = 4.3333333333
4 + 4x + x2 = 4.3333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.3333333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + 2) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + 2 = 2.081665999

Simplifying
x + 2 = 2.081665999

Reorder the terms:
2 + x = 2.081665999

Solving
2 + x = 2.081665999

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.081665999 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.081665999 + -2
x = 2.081665999 + -2

Combine like terms: 2.081665999 + -2 = 0.081665999
x = 0.081665999

Simplifying
x = 0.081665999


Subproblem 2
x + 2 = -2.081665999

Simplifying
x + 2 = -2.081665999

Reorder the terms:
2 + x = -2.081665999

Solving
2 + x = -2.081665999

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.081665999 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.081665999 + -2
x = -2.081665999 + -2

Combine like terms: -2.081665999 + -2 = -4.081665999
x = -4.081665999

Simplifying
x = -4.081665999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.081665999, -4.081665999}
Solution
x = {0.081665999, -4.081665999}

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