g^2=7g-12

Solution for g^2=7g-12 equation:

Simplifying
g2 = 7g + -12

Reorder the terms:
g2 = -12 + 7g

Solving
g2 = -12 + 7g

Solving for variable 'g'.

Reorder the terms:
12 + -7g + g2 = -12 + 7g + 12 + -7g

Reorder the terms:
12 + -7g + g2 = -12 + 12 + 7g + -7g

Combine like terms: -12 + 12 = 0
12 + -7g + g2 = 0 + 7g + -7g
12 + -7g + g2 = 7g + -7g

Combine like terms: 7g + -7g = 0
12 + -7g + g2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
g = {3, 4}