4n^2-32n-6=-8n-6

Solution for 4n^2-32n-6=-8n-6 equation:

Simplifying
4n2 + -32n + -6 = -8n + -6

Reorder the terms:
-6 + -32n + 4n2 = -8n + -6

Reorder the terms:
-6 + -32n + 4n2 = -6 + -8n

Add '6' to each side of the equation.
-6 + -32n + 6 + 4n2 = -6 + 6 + -8n

Reorder the terms:
-6 + 6 + -32n + 4n2 = -6 + 6 + -8n

Combine like terms: -6 + 6 = 0
0 + -32n + 4n2 = -6 + 6 + -8n
-32n + 4n2 = -6 + 6 + -8n

Combine like terms: -6 + 6 = 0
-32n + 4n2 = 0 + -8n
-32n + 4n2 = -8n

Solving
-32n + 4n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-32n + 8n + 4n2 = -8n + 8n

Combine like terms: -32n + 8n = -24n
-24n + 4n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-24n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4n'.
4n(-6 + n) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-6 + n)' equal to zero and attempt to solve:

Simplifying
-6 + n = 0

Solving
-6 + n = 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 + n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + n = 0 + 6
n = 0 + 6

Combine like terms: 0 + 6 = 6
n = 6

Simplifying
n = 6
Solution
n = {0, 6}