2n^2-n-9=-3

Solution for 2n^2-n-9=-3 equation:

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

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

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

Solving for variable 'n'.

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

Combine like terms: -9 + 3 = -6
-6 + -1n + 2n2 = -3 + 3

Combine like terms: -3 + 3 = 0
-6 + -1n + 2n2 = 0

Factor a trinomial.
(-3 + -2n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve:

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2n = 0 + 3

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

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

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-1.5, 2}