2g+6-14g=-6g(g-5)

Solution for 2g+6-14g=-6g(g-5) equation:

Simplifying
2g + 6 + -14g = -6g(g + -5)

Reorder the terms:
6 + 2g + -14g = -6g(g + -5)

Combine like terms: 2g + -14g = -12g
6 + -12g = -6g(g + -5)

Reorder the terms:
6 + -12g = -6g(-5 + g)
6 + -12g = (-5 * -6g + g * -6g)
6 + -12g = (30g + -6g2)

Solving
6 + -12g = 30g + -6g2

Solving for variable 'g'.

Combine like terms: -12g + -30g = -42g
6 + -42g + 6g2 = 30g + -6g2 + -30g + 6g2

Reorder the terms:
6 + -42g + 6g2 = 30g + -30g + -6g2 + 6g2

Combine like terms: 30g + -30g = 0
6 + -42g + 6g2 = 0 + -6g2 + 6g2
6 + -42g + 6g2 = -6g2 + 6g2

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

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -7g + g2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -7g + g2)' equal to zero and attempt to solve:

Simplifying
1 + -7g + g2 = 0

Solving
1 + -7g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7g + -1 + g2 = 0 + -1

Reorder the terms:
1 + -1 + -7g + g2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7g + g2 = 0 + -1
-7g + g2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7g + g2 = -1

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 + 12.25

Reorder the terms:
12.25 + -7g + g2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + -7g + g2 = 11.25

Factor a perfect square on the left side:
(g + -3.5)(g + -3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(g + -3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
g + -3.5 = 3.354101966

Simplifying
g + -3.5 = 3.354101966

Reorder the terms:
-3.5 + g = 3.354101966

Solving
-3.5 + g = 3.354101966

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 = 3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + g = 3.354101966 + 3.5
g = 3.354101966 + 3.5

Combine like terms: 3.354101966 + 3.5 = 6.854101966
g = 6.854101966

Simplifying
g = 6.854101966

Subproblem 2
g + -3.5 = -3.354101966

Simplifying
g + -3.5 = -3.354101966

Reorder the terms:
-3.5 + g = -3.354101966

Solving
-3.5 + g = -3.354101966

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 = -3.354101966 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + g = -3.354101966 + 3.5
g = -3.354101966 + 3.5

Combine like terms: -3.354101966 + 3.5 = 0.145898034
g = 0.145898034

Simplifying
g = 0.145898034

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {6.854101966, 0.145898034}
Solution
g = {6.854101966, 0.145898034}