120=2N+N^2

Solution for 120=2N+N^2 equation:

Simplifying
120 = 2N + N2

Solving
120 = 2N + N2

Solving for variable 'N'.

Reorder the terms:
120 + -2N + -1N2 = 2N + -2N + N2 + -1N2

Combine like terms: 2N + -2N = 0
120 + -2N + -1N2 = 0 + N2 + -1N2
120 + -2N + -1N2 = N2 + -1N2

Combine like terms: N2 + -1N2 = 0
120 + -2N + -1N2 = 0

Factor a trinomial.
(10 + -1N)(12 + N) = 0

Subproblem 1
Set the factor '(10 + -1N)' equal to zero and attempt to solve:

Simplifying
10 + -1N = 0

Solving
10 + -1N = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1N = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1N = 0 + -10
-1N = 0 + -10

Combine like terms: 0 + -10 = -10
-1N = -10

Divide each side by '-1'.
N = 10

Simplifying
N = 10
Subproblem 2
Set the factor '(12 + N)' equal to zero and attempt to solve:

Simplifying
12 + N = 0

Solving
12 + N = 0

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

Add '-12' to each side of the equation.
12 + -12 + N = 0 + -12

Combine like terms: 12 + -12 = 0
0 + N = 0 + -12
N = 0 + -12

Combine like terms: 0 + -12 = -12
N = -12

Simplifying
N = -12
Solution
N = {10, -12}