g^2-12g+6=-21

Solution for g^2-12g+6=-21 equation:

Simplifying
g2 + -12g + 6 = -21

Reorder the terms:
6 + -12g + g2 = -21

Solving
6 + -12g + g2 = -21

Solving for variable 'g'.

Reorder the terms:
6 + 21 + -12g + g2 = -21 + 21

Combine like terms: 6 + 21 = 27
27 + -12g + g2 = -21 + 21

Combine like terms: -21 + 21 = 0
27 + -12g + g2 = 0

Factor a trinomial.
(3 + -1g)(9 + -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 '(9 + -1g)' equal to zero and attempt to solve:

Simplifying
9 + -1g = 0

Solving
9 + -1g = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1g = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1g = 0 + -9
-1g = 0 + -9

Combine like terms: 0 + -9 = -9
-1g = -9

Divide each side by '-1'.
g = 9

Simplifying
g = 9
Solution
g = {3, 9}