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

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

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

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

Solving
-3g + g2 = 12 + -4g

Solving for variable 'g'.

Reorder the terms:
-12 + -3g + 4g + g2 = 12 + -4g + -12 + 4g

Combine like terms: -3g + 4g = 1g
-12 + 1g + g2 = 12 + -4g + -12 + 4g

Reorder the terms:
-12 + 1g + g2 = 12 + -12 + -4g + 4g

Combine like terms: 12 + -12 = 0
-12 + 1g + g2 = 0 + -4g + 4g
-12 + 1g + g2 = -4g + 4g

Combine like terms: -4g + 4g = 0
-12 + 1g + g2 = 0

Factor a trinomial.
(-4 + -1g)(3 + -1g) = 0

Subproblem 1
Set the factor '(-4 + -1g)' equal to zero and attempt to solve:

Simplifying
-4 + -1g = 0

Solving
-4 + -1g = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1g = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1g = 0 + 4
-1g = 0 + 4

Combine like terms: 0 + 4 = 4
-1g = 4

Divide each side by '-1'.
g = -4

Simplifying
g = -4
Subproblem 2
Set the factor '(3 + -1g)' equal to zero and attempt to solve:

Simplifying
3 + -1g = 0

Solving
3 + -1g = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1g = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1g = 0 + -3
-1g = 0 + -3

Combine like terms: 0 + -3 = -3
-1g = -3

Divide each side by '-1'.
g = 3

Simplifying
g = 3
Solution
g = {-4, 3}