3n^2+9n-89=1+2n^2

Solution for 3n^2+9n-89=1+2n^2 equation:

Simplifying
3n2 + 9n + -89 = 1 + 2n2

Reorder the terms:
-89 + 9n + 3n2 = 1 + 2n2

Solving
-89 + 9n + 3n2 = 1 + 2n2

Solving for variable 'n'.

Reorder the terms:
-89 + -1 + 9n + 3n2 + -2n2 = 1 + 2n2 + -1 + -2n2

Combine like terms: -89 + -1 = -90
-90 + 9n + 3n2 + -2n2 = 1 + 2n2 + -1 + -2n2

Combine like terms: 3n2 + -2n2 = 1n2
-90 + 9n + 1n2 = 1 + 2n2 + -1 + -2n2

Reorder the terms:
-90 + 9n + 1n2 = 1 + -1 + 2n2 + -2n2

Combine like terms: 1 + -1 = 0
-90 + 9n + 1n2 = 0 + 2n2 + -2n2
-90 + 9n + 1n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-90 + 9n + 1n2 = 0

Factor a trinomial.
(-15 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-15, 6}