6-3(2g+4)4g=5(1-2g)

Solution for 6-3(2g+4)4g=5(1-2g) equation:

Simplifying
6 + -3(2g + 4) * 4g = 5(1 + -2g)

Reorder the terms:
6 + -3(4 + 2g) * 4g = 5(1 + -2g)

Reorder the terms for easier multiplication:
6 + -3 * 4g(4 + 2g) = 5(1 + -2g)

Multiply -3 * 4
6 + -12g(4 + 2g) = 5(1 + -2g)
6 + (4 * -12g + 2g * -12g) = 5(1 + -2g)
6 + (-48g + -24g2) = 5(1 + -2g)
6 + -48g + -24g2 = (1 * 5 + -2g * 5)
6 + -48g + -24g2 = (5 + -10g)

Solving
6 + -48g + -24g2 = 5 + -10g

Solving for variable 'g'.

Reorder the terms:
6 + -5 + -48g + 10g + -24g2 = 5 + -10g + -5 + 10g

Combine like terms: 6 + -5 = 1
1 + -48g + 10g + -24g2 = 5 + -10g + -5 + 10g

Combine like terms: -48g + 10g = -38g
1 + -38g + -24g2 = 5 + -10g + -5 + 10g

Reorder the terms:
1 + -38g + -24g2 = 5 + -5 + -10g + 10g

Combine like terms: 5 + -5 = 0
1 + -38g + -24g2 = 0 + -10g + 10g
1 + -38g + -24g2 = -10g + 10g

Combine like terms: -10g + 10g = 0
1 + -38g + -24g2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-0.04166666667 + 1.583333333g + g2 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 1.583333333g + 0.04166666667 + g2 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + 1.583333333g + g2 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + 1.583333333g + g2 = 0 + 0.04166666667
1.583333333g + g2 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
1.583333333g + g2 = 0.04166666667

The g term is 1.583333333g.  Take half its coefficient (0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
1.583333333g + 0.6267361108 + g2 = 0.04166666667 + 0.6267361108

Reorder the terms:
0.6267361108 + 1.583333333g + g2 = 0.04166666667 + 0.6267361108

Combine like terms: 0.04166666667 + 0.6267361108 = 0.66840277747
0.6267361108 + 1.583333333g + g2 = 0.66840277747

Factor a perfect square on the left side:
(g + 0.7916666665)(g + 0.7916666665) = 0.66840277747

Calculate the square root of the right side: 0.817559036

Break this problem into two subproblems by setting 
(g + 0.7916666665) equal to 0.817559036 and -0.817559036.

Subproblem 1
g + 0.7916666665 = 0.817559036

Simplifying
g + 0.7916666665 = 0.817559036

Reorder the terms:
0.7916666665 + g = 0.817559036

Solving
0.7916666665 + g = 0.817559036

Solving for variable 'g'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + g = 0.817559036 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + g = 0.817559036 + -0.7916666665
g = 0.817559036 + -0.7916666665

Combine like terms: 0.817559036 + -0.7916666665 = 0.0258923695
g = 0.0258923695

Simplifying
g = 0.0258923695

Subproblem 2
g + 0.7916666665 = -0.817559036

Simplifying
g + 0.7916666665 = -0.817559036

Reorder the terms:
0.7916666665 + g = -0.817559036

Solving
0.7916666665 + g = -0.817559036

Solving for variable 'g'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + g = -0.817559036 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + g = -0.817559036 + -0.7916666665
g = -0.817559036 + -0.7916666665

Combine like terms: -0.817559036 + -0.7916666665 = -1.6092257025
g = -1.6092257025

Simplifying
g = -1.6092257025

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.0258923695, -1.6092257025}