n^2+3n+2=210

Solution for n^2+3n+2=210 equation:

Simplifying
n2 + 3n + 2 = 210

Reorder the terms:
2 + 3n + n2 = 210

Solving
2 + 3n + n2 = 210

Solving for variable 'n'.

Reorder the terms:
2 + -210 + 3n + n2 = 210 + -210

Combine like terms: 2 + -210 = -208
-208 + 3n + n2 = 210 + -210

Combine like terms: 210 + -210 = 0
-208 + 3n + n2 = 0

Factor a trinomial.
(-16 + -1n)(13 + -1n) = 0

Subproblem 1
Set the factor '(-16 + -1n)' equal to zero and attempt to solve:

Simplifying
-16 + -1n = 0

Solving
-16 + -1n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1n = 0 + 16
-1n = 0 + 16

Combine like terms: 0 + 16 = 16
-1n = 16

Divide each side by '-1'.
n = -16

Simplifying
n = -16
Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-16, 13}