n^2-2n-66=-3

Solution for n^2-2n-66=-3 equation:

Simplifying
n2 + -2n + -66 = -3

Reorder the terms:
-66 + -2n + n2 = -3

Solving
-66 + -2n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
-66 + 3 + -2n + n2 = -3 + 3

Combine like terms: -66 + 3 = -63
-63 + -2n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
-63 + -2n + n2 = 0

Factor a trinomial.
(-7 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-7, 9}