8n^2+32n=168

Solution for 8n^2+32n=168 equation:

Simplifying
8n2 + 32n = 168

Reorder the terms:
32n + 8n2 = 168

Solving
32n + 8n2 = 168

Solving for variable 'n'.

Reorder the terms:
-168 + 32n + 8n2 = 168 + -168

Combine like terms: 168 + -168 = 0
-168 + 32n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-21 + 4n + n2) = 0

Factor a trinomial.
8((-7 + -1n)(3 + -1n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-7, 3}