2N^2-9N=5

Solution for 2N^2-9N=5 equation:

Simplifying
2N2 + -9N = 5

Reorder the terms:
-9N + 2N2 = 5

Solving
-9N + 2N2 = 5

Solving for variable 'N'.

Reorder the terms:
-5 + -9N + 2N2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -9N + 2N2 = 0

Factor a trinomial.
(-1 + -2N)(5 + -1N) = 0

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

Simplifying
-1 + -2N = 0

Solving
-1 + -2N = 0

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

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

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

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

Divide each side by '-2'.
N = -0.5

Simplifying
N = -0.5
Subproblem 2
Set the factor '(5 + -1N)' equal to zero and attempt to solve:

Simplifying
5 + -1N = 0

Solving
5 + -1N = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1N = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1N = 0 + -5
-1N = 0 + -5

Combine like terms: 0 + -5 = -5
-1N = -5

Divide each side by '-1'.
N = 5

Simplifying
N = 5
Solution
N = {-0.5, 5}