g^2-13g+40=0

Solution for g^2-13g+40=0 equation:

Simplifying
g2 + -13g + 40 = 0

Reorder the terms:
40 + -13g + g2 = 0

Solving
40 + -13g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(5 + -1g)(8 + -1g) = 0

Subproblem 1
Set the factor '(5 + -1g)' equal to zero and attempt to solve:

Simplifying
5 + -1g = 0

Solving
5 + -1g = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1g = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1g = 0 + -5
-1g = 0 + -5

Combine like terms: 0 + -5 = -5
-1g = -5

Divide each side by '-1'.
g = 5

Simplifying
g = 5
Subproblem 2
Set the factor '(8 + -1g)' equal to zero and attempt to solve:

Simplifying
8 + -1g = 0

Solving
8 + -1g = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1g = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1g = 0 + -8
-1g = 0 + -8

Combine like terms: 0 + -8 = -8
-1g = -8

Divide each side by '-1'.
g = 8

Simplifying
g = 8
Solution
g = {5, 8}