2n^2-5n-22=-4

Solution for 2n^2-5n-22=-4 equation:

Simplifying
2n2 + -5n + -22 = -4

Reorder the terms:
-22 + -5n + 2n2 = -4

Solving
-22 + -5n + 2n2 = -4

Solving for variable 'n'.

Reorder the terms:
-22 + 4 + -5n + 2n2 = -4 + 4

Combine like terms: -22 + 4 = -18
-18 + -5n + 2n2 = -4 + 4

Combine like terms: -4 + 4 = 0
-18 + -5n + 2n2 = 0

Factor a trinomial.
(-2 + -1n)(9 + -2n) = 0

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

Simplifying
9 + -2n = 0

Solving
9 + -2n = 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 + -2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2n = 0 + -9
-2n = 0 + -9

Combine like terms: 0 + -9 = -9
-2n = -9

Divide each side by '-2'.
n = 4.5

Simplifying
n = 4.5
Solution
n = {-2, 4.5}