N^2+N-59=-3

Solution for N^2+N-59=-3 equation:

Simplifying
N2 + N + -59 = -3

Reorder the terms:
-59 + N + N2 = -3

Solving
-59 + N + N2 = -3

Solving for variable 'N'.

Reorder the terms:
-59 + 3 + N + N2 = -3 + 3

Combine like terms: -59 + 3 = -56
-56 + N + N2 = -3 + 3

Combine like terms: -3 + 3 = 0
-56 + N + N2 = 0

Factor a trinomial.
(-8 + -1N)(7 + -1N) = 0

Subproblem 1
Set the factor '(-8 + -1N)' equal to zero and attempt to solve:

Simplifying
-8 + -1N = 0

Solving
-8 + -1N = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1N = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1N = 0 + 8
-1N = 0 + 8

Combine like terms: 0 + 8 = 8
-1N = 8

Divide each side by '-1'.
N = -8

Simplifying
N = -8
Subproblem 2
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
Solution
N = {-8, 7}