4g(16+2g)=8g+12

Solution for 4g(16+2g)=8g+12 equation:

Simplifying
4g(16 + 2g) = 8g + 12
(16 * 4g + 2g * 4g) = 8g + 12
(64g + 8g2) = 8g + 12

Reorder the terms:
64g + 8g2 = 12 + 8g

Solving
64g + 8g2 = 12 + 8g

Solving for variable 'g'.

Reorder the terms:
-12 + 64g + -8g + 8g2 = 12 + 8g + -12 + -8g

Combine like terms: 64g + -8g = 56g
-12 + 56g + 8g2 = 12 + 8g + -12 + -8g

Reorder the terms:
-12 + 56g + 8g2 = 12 + -12 + 8g + -8g

Combine like terms: 12 + -12 = 0
-12 + 56g + 8g2 = 0 + 8g + -8g
-12 + 56g + 8g2 = 8g + -8g

Combine like terms: 8g + -8g = 0
-12 + 56g + 8g2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 14g + 2g2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 14g + 2g2)' equal to zero and attempt to solve:

Simplifying
-3 + 14g + 2g2 = 0

Solving
-3 + 14g + 2g2 = 0

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

Divide each side by '2'.
-1.5 + 7g + g2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 7g + 1.5 + g2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 7g + g2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 7g + g2 = 0 + 1.5
7g + g2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
7g + g2 = 1.5

The g term is 7g.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7g + 12.25 + g2 = 1.5 + 12.25

Reorder the terms:
12.25 + 7g + g2 = 1.5 + 12.25

Combine like terms: 1.5 + 12.25 = 13.75
12.25 + 7g + g2 = 13.75

Factor a perfect square on the left side:
(g + 3.5)(g + 3.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(g + 3.5) equal to 3.708099244 and -3.708099244.

Subproblem 1
g + 3.5 = 3.708099244

Simplifying
g + 3.5 = 3.708099244

Reorder the terms:
3.5 + g = 3.708099244

Solving
3.5 + g = 3.708099244

Solving for variable 'g'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + g = 3.708099244 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = 3.708099244 + -3.5
g = 3.708099244 + -3.5

Combine like terms: 3.708099244 + -3.5 = 0.208099244
g = 0.208099244

Simplifying
g = 0.208099244

Subproblem 2
g + 3.5 = -3.708099244

Simplifying
g + 3.5 = -3.708099244

Reorder the terms:
3.5 + g = -3.708099244

Solving
3.5 + g = -3.708099244

Solving for variable 'g'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + g = -3.708099244 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = -3.708099244 + -3.5
g = -3.708099244 + -3.5

Combine like terms: -3.708099244 + -3.5 = -7.208099244
g = -7.208099244

Simplifying
g = -7.208099244

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.208099244, -7.208099244}
Solution
g = {0.208099244, -7.208099244}