n^2-n-10=10

Solution for n^2-n-10=10 equation:

Simplifying
n2 + -1n + -10 = 10

Reorder the terms:
-10 + -1n + n2 = 10

Solving
-10 + -1n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -10 + -1n + n2 = 10 + -10

Combine like terms: -10 + -10 = -20
-20 + -1n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-20 + -1n + n2 = 0

Factor a trinomial.
(-4 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
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
Solution
n = {-4, 5}