4n^2-2n+6=12

Solution for 4n^2-2n+6=12 equation:

Simplifying
4n2 + -2n + 6 = 12

Reorder the terms:
6 + -2n + 4n2 = 12

Solving
6 + -2n + 4n2 = 12

Solving for variable 'n'.

Reorder the terms:
6 + -12 + -2n + 4n2 = 12 + -12

Combine like terms: 6 + -12 = -6
-6 + -2n + 4n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-6 + -2n + 4n2 = 0

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

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

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-1, 1.5}