6(7-2g)g=3

Solution for 6(7-2g)g=3 equation:

Simplifying
6(7 + -2g) * g = 3

Reorder the terms for easier multiplication:
6g(7 + -2g) = 3
(7 * 6g + -2g * 6g) = 3
(42g + -12g2) = 3

Solving
42g + -12g2 = 3

Solving for variable 'g'.

Reorder the terms:
-3 + 42g + -12g2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 42g + -12g2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 14g + -4g2) = 0

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

Simplifying
-1 + 14g + -4g2 = 0

Solving
-1 + 14g + -4g2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -3.5g + g2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -3.5g + -0.25 + g2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -3.5g + g2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -3.5g + g2 = 0 + -0.25
-3.5g + g2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-3.5g + g2 = -0.25

The g term is -3.5g.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5g + 3.0625 + g2 = -0.25 + 3.0625

Reorder the terms:
3.0625 + -3.5g + g2 = -0.25 + 3.0625

Combine like terms: -0.25 + 3.0625 = 2.8125
3.0625 + -3.5g + g2 = 2.8125

Factor a perfect square on the left side:
(g + -1.75)(g + -1.75) = 2.8125

Calculate the square root of the right side: 1.677050983

Break this problem into two subproblems by setting 
(g + -1.75) equal to 1.677050983 and -1.677050983.

Subproblem 1
g + -1.75 = 1.677050983

Simplifying
g + -1.75 = 1.677050983

Reorder the terms:
-1.75 + g = 1.677050983

Solving
-1.75 + g = 1.677050983

Solving for variable 'g'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + g = 1.677050983 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + g = 1.677050983 + 1.75
g = 1.677050983 + 1.75

Combine like terms: 1.677050983 + 1.75 = 3.427050983
g = 3.427050983

Simplifying
g = 3.427050983

Subproblem 2
g + -1.75 = -1.677050983

Simplifying
g + -1.75 = -1.677050983

Reorder the terms:
-1.75 + g = -1.677050983

Solving
-1.75 + g = -1.677050983

Solving for variable 'g'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + g = -1.677050983 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + g = -1.677050983 + 1.75
g = -1.677050983 + 1.75

Combine like terms: -1.677050983 + 1.75 = 0.072949017
g = 0.072949017

Simplifying
g = 0.072949017

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {3.427050983, 0.072949017}
Solution
g = {3.427050983, 0.072949017}