8n^2+4-12n=0

Solution for 8n^2+4-12n=0 equation:

Simplifying
8n2 + 4 + -12n = 0

Reorder the terms:
4 + -12n + 8n2 = 0

Solving
4 + -12n + 8n2 = 0

Solving for variable 'n'.

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

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

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
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 = {0.5, 1}