G^1(x)=ax(2b-3x)

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Solution for G^1(x)=ax(2b-3x) equation: 


Simplifying
G(x) = ax(2b + -3x)

Multiply G * x
xG = ax(2b + -3x)
xG = (2b * ax + -3x * ax)
xG = (2abx + -3ax2)

Solving
xG = 2abx + -3ax2

Solving for variable 'x'.

Reorder the terms:
-2abx + 3ax2 + xG = 2abx + -3ax2 + -2abx + 3ax2

Reorder the terms:
-2abx + 3ax2 + xG = 2abx + -2abx + -3ax2 + 3ax2

Combine like terms: 2abx + -2abx = 0
-2abx + 3ax2 + xG = 0 + -3ax2 + 3ax2
-2abx + 3ax2 + xG = -3ax2 + 3ax2

Combine like terms: -3ax2 + 3ax2 = 0
-2abx + 3ax2 + xG = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2ab + 3ax + G) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-2ab + 3ax + G)' equal to zero and attempt to solve:

Simplifying
-2ab + 3ax + G = 0

Reorder the terms:
G + -2ab + 3ax = 0

Solving
G + -2ab + 3ax = 0

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

Add '-1G' to each side of the equation.
G + -2ab + -1G + 3ax = 0 + -1G

Reorder the terms:
G + -1G + -2ab + 3ax = 0 + -1G

Combine like terms: G + -1G = 0
0 + -2ab + 3ax = 0 + -1G
-2ab + 3ax = 0 + -1G
Remove the zero:
-2ab + 3ax = -1G

Add '2ab' to each side of the equation.
-2ab + 2ab + 3ax = -1G + 2ab

Combine like terms: -2ab + 2ab = 0
0 + 3ax = -1G + 2ab
3ax = -1G + 2ab

Divide each side by '3a'.
x = -0.3333333333a-1G + 0.6666666667b

Simplifying
x = -0.3333333333a-1G + 0.6666666667b
Solution
x = {0, -0.3333333333a-1G + 0.6666666667b}

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