g^2-5g=-6

Solution for g^2-5g=-6 equation:

Simplifying
g2 + -5g = -6

Reorder the terms:
-5g + g2 = -6

Solving
-5g + g2 = -6

Solving for variable 'g'.

Reorder the terms:
6 + -5g + g2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -5g + g2 = 0

Factor a trinomial.
(2 + -1g)(3 + -1g) = 0

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

Simplifying
2 + -1g = 0

Solving
2 + -1g = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1g = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g = 0 + -2
-1g = 0 + -2

Combine like terms: 0 + -2 = -2
-1g = -2

Divide each side by '-1'.
g = 2

Simplifying
g = 2
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 = {2, 3}