3g^2-12g-4=0

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Solution for 3g^2-12g-4=0 equation: 


Simplifying
3g2 + -12g + -4 = 0

Reorder the terms:
-4 + -12g + 3g2 = 0

Solving
-4 + -12g + 3g2 = 0

Solving for variable 'g'.

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

Divide each side by '3'.
-1.333333333 + -4g + g2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -4g + 1.333333333 + g2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -4g + g2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -4g + g2 = 0 + 1.333333333
-4g + g2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-4g + g2 = 1.333333333

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

Add '4' to each side of the equation.
-4g + 4 + g2 = 1.333333333 + 4

Reorder the terms:
4 + -4g + g2 = 1.333333333 + 4

Combine like terms: 1.333333333 + 4 = 5.333333333
4 + -4g + g2 = 5.333333333

Factor a perfect square on the left side:
(g + -2)(g + -2) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(g + -2) equal to 2.309401077 and -2.309401077.


Subproblem 1
g + -2 = 2.309401077

Simplifying
g + -2 = 2.309401077

Reorder the terms:
-2 + g = 2.309401077

Solving
-2 + g = 2.309401077

Solving for variable 'g'.

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

Add '2' to each side of the equation.
-2 + 2 + g = 2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + g = 2.309401077 + 2
g = 2.309401077 + 2

Combine like terms: 2.309401077 + 2 = 4.309401077
g = 4.309401077

Simplifying
g = 4.309401077


Subproblem 2
g + -2 = -2.309401077

Simplifying
g + -2 = -2.309401077

Reorder the terms:
-2 + g = -2.309401077

Solving
-2 + g = -2.309401077

Solving for variable 'g'.

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

Add '2' to each side of the equation.
-2 + 2 + g = -2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + g = -2.309401077 + 2
g = -2.309401077 + 2

Combine like terms: -2.309401077 + 2 = -0.309401077
g = -0.309401077

Simplifying
g = -0.309401077


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {4.309401077, -0.309401077}

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