-2g(g+6)=g+3+2g

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

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

Reorder the terms:
-2g(6 + g) = g + 3 + 2g
(6 * -2g + g * -2g) = g + 3 + 2g
(-12g + -2g2) = g + 3 + 2g

Reorder the terms:
-12g + -2g2 = 3 + g + 2g

Combine like terms: g + 2g = 3g
-12g + -2g2 = 3 + 3g

Solving
-12g + -2g2 = 3 + 3g

Solving for variable 'g'.

Reorder the terms:
-3 + -12g + -3g + -2g2 = 3 + 3g + -3 + -3g

Combine like terms: -12g + -3g = -15g
-3 + -15g + -2g2 = 3 + 3g + -3 + -3g

Reorder the terms:
-3 + -15g + -2g2 = 3 + -3 + 3g + -3g

Combine like terms: 3 + -3 = 0
-3 + -15g + -2g2 = 0 + 3g + -3g
-3 + -15g + -2g2 = 3g + -3g

Combine like terms: 3g + -3g = 0
-3 + -15g + -2g2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 15g + 2g2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 15g + 2g2)' equal to zero and attempt to solve:

Simplifying
3 + 15g + 2g2 = 0

Solving
3 + 15g + 2g2 = 0

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

Divide each side by '2'.
1.5 + 7.5g + g2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 7.5g + -1.5 + g2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 7.5g + g2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 7.5g + g2 = 0 + -1.5
7.5g + g2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
7.5g + g2 = -1.5

The g term is 7.5g.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5g + 14.0625 + g2 = -1.5 + 14.0625

Reorder the terms:
14.0625 + 7.5g + g2 = -1.5 + 14.0625

Combine like terms: -1.5 + 14.0625 = 12.5625
14.0625 + 7.5g + g2 = 12.5625

Factor a perfect square on the left side:
(g + 3.75)(g + 3.75) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(g + 3.75) equal to 3.54436172 and -3.54436172.

Subproblem 1
g + 3.75 = 3.54436172

Simplifying
g + 3.75 = 3.54436172

Reorder the terms:
3.75 + g = 3.54436172

Solving
3.75 + g = 3.54436172

Solving for variable 'g'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + g = 3.54436172 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + g = 3.54436172 + -3.75
g = 3.54436172 + -3.75

Combine like terms: 3.54436172 + -3.75 = -0.20563828
g = -0.20563828

Simplifying
g = -0.20563828

Subproblem 2
g + 3.75 = -3.54436172

Simplifying
g + 3.75 = -3.54436172

Reorder the terms:
3.75 + g = -3.54436172

Solving
3.75 + g = -3.54436172

Solving for variable 'g'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + g = -3.54436172 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + g = -3.54436172 + -3.75
g = -3.54436172 + -3.75

Combine like terms: -3.54436172 + -3.75 = -7.29436172
g = -7.29436172

Simplifying
g = -7.29436172

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-0.20563828, -7.29436172}
Solution
g = {-0.20563828, -7.29436172}