6n^2-8n=128

Solution for 6n^2-8n=128 equation:

Simplifying
6n2 + -8n = 128

Reorder the terms:
-8n + 6n2 = 128

Solving
-8n + 6n2 = 128

Solving for variable 'n'.

Reorder the terms:
-128 + -8n + 6n2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + -8n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-64 + -4n + 3n2) = 0

Factor a trinomial.
2((-4 + -1n)(16 + -3n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(16 + -3n)' equal to zero and attempt to solve:

Simplifying
16 + -3n = 0

Solving
16 + -3n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3n = 0 + -16
-3n = 0 + -16

Combine like terms: 0 + -16 = -16
-3n = -16

Divide each side by '-3'.
n = 5.333333333

Simplifying
n = 5.333333333
Solution
n = {-4, 5.333333333}