n^2-7n-30=30

Solution for n^2-7n-30=30 equation:

Simplifying
n2 + -7n + -30 = 30

Reorder the terms:
-30 + -7n + n2 = 30

Solving
-30 + -7n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -30 + -7n + n2 = 30 + -30

Combine like terms: -30 + -30 = -60
-60 + -7n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-60 + -7n + n2 = 0

Factor a trinomial.
(-5 + -1n)(12 + -1n) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

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

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

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

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

Simplifying
n = -5
Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {-5, 12}