n^2=n+30

Solution for n^2=n+30 equation:

Simplifying
n2 = n + 30

Reorder the terms:
n2 = 30 + n

Solving
n2 = 30 + n

Solving for variable 'n'.

Reorder the terms:
-30 + -1n + n2 = 30 + n + -30 + -1n

Reorder the terms:
-30 + -1n + n2 = 30 + -30 + n + -1n

Combine like terms: 30 + -30 = 0
-30 + -1n + n2 = 0 + n + -1n
-30 + -1n + n2 = n + -1n

Combine like terms: n + -1n = 0
-30 + -1n + n2 = 0

Factor a trinomial.
(-5 + -1n)(6 + -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 '(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 = {-5, 6}