n^2-6n-45=10

Solution for n^2-6n-45=10 equation:

Simplifying
n2 + -6n + -45 = 10

Reorder the terms:
-45 + -6n + n2 = 10

Solving
-45 + -6n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
-45 + -10 + -6n + n2 = 10 + -10

Combine like terms: -45 + -10 = -55
-55 + -6n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-55 + -6n + n2 = 0

Factor a trinomial.
(-5 + -1n)(11 + -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 '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-5, 11}