n^2+7n=78

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

Simplifying
n2 + 7n = 78

Reorder the terms:
7n + n2 = 78

Solving
7n + n2 = 78

Solving for variable 'n'.

Reorder the terms:
-78 + 7n + n2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 7n + n2 = 0

Factor a trinomial.
(-13 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -1n)' equal to zero and attempt to solve:

Simplifying
-13 + -1n = 0

Solving
-13 + -1n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1n = 0 + 13
-1n = 0 + 13

Combine like terms: 0 + 13 = 13
-1n = 13

Divide each side by '-1'.
n = -13

Simplifying
n = -13
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

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

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

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

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

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