6g(g+7)=8

Solution for 6g(g+7)=8 equation:

Simplifying
6g(g + 7) = 8

Reorder the terms:
6g(7 + g) = 8
(7 * 6g + g * 6g) = 8
(42g + 6g2) = 8

Solving
42g + 6g2 = 8

Solving for variable 'g'.

Reorder the terms:
-8 + 42g + 6g2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 42g + 6g2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 21g + 3g2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 21g + 3g2)' equal to zero and attempt to solve:

Simplifying
-4 + 21g + 3g2 = 0

Solving
-4 + 21g + 3g2 = 0

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

Divide each side by '3'.
-1.333333333 + 7g + g2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 7g + 1.333333333 + g2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 7g + g2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 7g + g2 = 0 + 1.333333333
7g + g2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
7g + g2 = 1.333333333

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 = 1.333333333 + 12.25

Reorder the terms:
12.25 + 7g + g2 = 1.333333333 + 12.25

Combine like terms: 1.333333333 + 12.25 = 13.583333333
12.25 + 7g + g2 = 13.583333333

Factor a perfect square on the left side:
(g + 3.5)(g + 3.5) = 13.583333333

Calculate the square root of the right side: 3.685557398

Break this problem into two subproblems by setting 
(g + 3.5) equal to 3.685557398 and -3.685557398.

Subproblem 1
g + 3.5 = 3.685557398

Simplifying
g + 3.5 = 3.685557398

Reorder the terms:
3.5 + g = 3.685557398

Solving
3.5 + g = 3.685557398

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 = 3.685557398 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = 3.685557398 + -3.5
g = 3.685557398 + -3.5

Combine like terms: 3.685557398 + -3.5 = 0.185557398
g = 0.185557398

Simplifying
g = 0.185557398

Subproblem 2
g + 3.5 = -3.685557398

Simplifying
g + 3.5 = -3.685557398

Reorder the terms:
3.5 + g = -3.685557398

Solving
3.5 + g = -3.685557398

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 = -3.685557398 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + g = -3.685557398 + -3.5
g = -3.685557398 + -3.5

Combine like terms: -3.685557398 + -3.5 = -7.185557398
g = -7.185557398

Simplifying
g = -7.185557398

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.185557398, -7.185557398}
Solution
g = {0.185557398, -7.185557398}