12n^2-4=8n

Solution for 12n^2-4=8n equation:

Simplifying
12n2 + -4 = 8n

Reorder the terms:
-4 + 12n2 = 8n

Solving
-4 + 12n2 = 8n

Solving for variable 'n'.

Reorder the terms:
-4 + -8n + 12n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-4 + -8n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -2n + 3n2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -3n)' equal to zero and attempt to solve:

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 0

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

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

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

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

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-0.3333333333, 1}