g^2+7g=78

Solution for g^2+7g=78 equation:

Simplifying
g2 + 7g = 78

Reorder the terms:
7g + g2 = 78

Solving
7g + g2 = 78

Solving for variable 'g'.

Reorder the terms:
-78 + 7g + g2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 7g + g2 = 0

Factor a trinomial.
(-13 + -1g)(6 + -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 '(6 + -1g)' equal to zero and attempt to solve:

Simplifying
6 + -1g = 0

Solving
6 + -1g = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1g = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1g = 0 + -6
-1g = 0 + -6

Combine like terms: 0 + -6 = -6
-1g = -6

Divide each side by '-1'.
g = 6

Simplifying
g = 6
Solution
g = {-13, 6}