2n^2+11n-45=-2n^2

Solution for 2n^2+11n-45=-2n^2 equation:

Simplifying
2n2 + 11n + -45 = -2n2

Reorder the terms:
-45 + 11n + 2n2 = -2n2

Solving
-45 + 11n + 2n2 = -2n2

Solving for variable 'n'.

Combine like terms: 2n2 + 2n2 = 4n2
-45 + 11n + 4n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-45 + 11n + 4n2 = 0

Factor a trinomial.
(-5 + -1n)(9 + -4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -4n)' equal to zero and attempt to solve:

Simplifying
9 + -4n = 0

Solving
9 + -4n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4n = 0 + -9
-4n = 0 + -9

Combine like terms: 0 + -9 = -9
-4n = -9

Divide each side by '-4'.
n = 2.25

Simplifying
n = 2.25
Solution
n = {-5, 2.25}