4g(g-3)-2g(g-2)=2(g+3)-6g-2

Solution for 4g(g-3)-2g(g-2)=2(g+3)-6g-2 equation:

Simplifying
4g(g + -3) + -2g(g + -2) = 2(g + 3) + -6g + -2

Reorder the terms:
4g(-3 + g) + -2g(g + -2) = 2(g + 3) + -6g + -2
(-3 * 4g + g * 4g) + -2g(g + -2) = 2(g + 3) + -6g + -2
(-12g + 4g2) + -2g(g + -2) = 2(g + 3) + -6g + -2

Reorder the terms:
-12g + 4g2 + -2g(-2 + g) = 2(g + 3) + -6g + -2
-12g + 4g2 + (-2 * -2g + g * -2g) = 2(g + 3) + -6g + -2
-12g + 4g2 + (4g + -2g2) = 2(g + 3) + -6g + -2

Reorder the terms:
-12g + 4g + 4g2 + -2g2 = 2(g + 3) + -6g + -2

Combine like terms: -12g + 4g = -8g
-8g + 4g2 + -2g2 = 2(g + 3) + -6g + -2

Combine like terms: 4g2 + -2g2 = 2g2
-8g + 2g2 = 2(g + 3) + -6g + -2

Reorder the terms:
-8g + 2g2 = 2(3 + g) + -6g + -2
-8g + 2g2 = (3 * 2 + g * 2) + -6g + -2
-8g + 2g2 = (6 + 2g) + -6g + -2

Reorder the terms:
-8g + 2g2 = 6 + -2 + 2g + -6g

Combine like terms: 6 + -2 = 4
-8g + 2g2 = 4 + 2g + -6g

Combine like terms: 2g + -6g = -4g
-8g + 2g2 = 4 + -4g

Solving
-8g + 2g2 = 4 + -4g

Solving for variable 'g'.

Reorder the terms:
-4 + -8g + 4g + 2g2 = 4 + -4g + -4 + 4g

Combine like terms: -8g + 4g = -4g
-4 + -4g + 2g2 = 4 + -4g + -4 + 4g

Reorder the terms:
-4 + -4g + 2g2 = 4 + -4 + -4g + 4g

Combine like terms: 4 + -4 = 0
-4 + -4g + 2g2 = 0 + -4g + 4g
-4 + -4g + 2g2 = -4g + 4g

Combine like terms: -4g + 4g = 0
-4 + -4g + 2g2 = 0

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

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

Simplifying
-2 + -2g + g2 = 0

Solving
-2 + -2g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2g + 2 + g2 = 0 + 2

Reorder the terms:
-2 + 2 + -2g + g2 = 0 + 2

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

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

The g term is -2g.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2g + 1 + g2 = 2 + 1

Reorder the terms:
1 + -2g + g2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + -2g + g2 = 3

Factor a perfect square on the left side:
(g + -1)(g + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(g + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
g + -1 = 1.732050808

Simplifying
g + -1 = 1.732050808

Reorder the terms:
-1 + g = 1.732050808

Solving
-1 + g = 1.732050808

Solving for variable 'g'.

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

Add '1' to each side of the equation.
-1 + 1 + g = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + g = 1.732050808 + 1
g = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
g = 2.732050808

Simplifying
g = 2.732050808

Subproblem 2
g + -1 = -1.732050808

Simplifying
g + -1 = -1.732050808

Reorder the terms:
-1 + g = -1.732050808

Solving
-1 + g = -1.732050808

Solving for variable 'g'.

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

Add '1' to each side of the equation.
-1 + 1 + g = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + g = -1.732050808 + 1
g = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
g = -0.732050808

Simplifying
g = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {2.732050808, -0.732050808}
Solution
g = {2.732050808, -0.732050808}