2n^2-8n=24

Solution for 2n^2-8n=24 equation:

Simplifying
2n2 + -8n = 24

Reorder the terms:
-8n + 2n2 = 24

Solving
-8n + 2n2 = 24

Solving for variable 'n'.

Reorder the terms:
-24 + -8n + 2n2 = 24 + -24

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

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

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

Ignore the factor 2.
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 '(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
Solution
n = {-2, 6}