Simplifying
g^{2} = 13 + -12g
Solving
g^{2} = 13 + -12g
Solving for variable 'g'.
Reorder the terms:
-13 + 12g + g^{2} = 13 + -12g + -13 + 12g
Reorder the terms:
-13 + 12g + g^{2} = 13 + -13 + -12g + 12g
Combine like terms: 13 + -13 = 0
-13 + 12g + g^{2} = 0 + -12g + 12g
-13 + 12g + g^{2} = -12g + 12g
Combine like terms: -12g + 12g = 0
-13 + 12g + g^{2} = 0
Factor a trinomial.
(-13 + -1g)(1 + -1g) = 0
#### Subproblem 1

Set the factor '(-13 + -1g)' equal to zero and attempt to solve:
Simplifying
-13 + -1g = 0
Solving
-13 + -1g = 0
Move all terms containing g to the left, all other terms to the right.
Add '13' to each side of the equation.
-13 + 13 + -1g = 0 + 13
Combine like terms: -13 + 13 = 0
0 + -1g = 0 + 13
-1g = 0 + 13
Combine like terms: 0 + 13 = 13
-1g = 13
Divide each side by '-1'.
g = -13
Simplifying
g = -13
#### Subproblem 2

Set the factor '(1 + -1g)' equal to zero and attempt to solve:
Simplifying
1 + -1g = 0
Solving
1 + -1g = 0
Move all terms containing g to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1g = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1g = 0 + -1
-1g = 0 + -1
Combine like terms: 0 + -1 = -1
-1g = -1
Divide each side by '-1'.
g = 1
Simplifying
g = 1#### Solution

g = {-13, 1}