2n^2+8n-22=2

Solution for 2n^2+8n-22=2 equation:

Simplifying
2n2 + 8n + -22 = 2

Reorder the terms:
-22 + 8n + 2n2 = 2

Solving
-22 + 8n + 2n2 = 2

Solving for variable 'n'.

Reorder the terms:
-22 + -2 + 8n + 2n2 = 2 + -2

Combine like terms: -22 + -2 = -24
-24 + 8n + 2n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-24 + 8n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4n + n2) = 0

Factor a trinomial.
2((-6 + -1n)(2 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-6, 2}