=2(n^2-7n+12)

Solution for =2(n^2-7n+12) equation:

Simplifying
0 = 2(n2 + -7n + 12)

Reorder the terms:
0 = 2(12 + -7n + n2)
0 = (12 * 2 + -7n * 2 + n2 * 2)
0 = (24 + -14n + 2n2)

Solving
0 = 24 + -14n + 2n2

Solving for variable 'n'.

Combine like terms: 0 + -24 = -24
-24 + 14n + -2n2 = 24 + -14n + 2n2 + -24 + 14n + -2n2

Reorder the terms:
-24 + 14n + -2n2 = 24 + -24 + -14n + 14n + 2n2 + -2n2

Combine like terms: 24 + -24 = 0
-24 + 14n + -2n2 = 0 + -14n + 14n + 2n2 + -2n2
-24 + 14n + -2n2 = -14n + 14n + 2n2 + -2n2

Combine like terms: -14n + 14n = 0
-24 + 14n + -2n2 = 0 + 2n2 + -2n2
-24 + 14n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-24 + 14n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 7n + -1n2) = 0

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

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

Simplifying
-4 + n = 0

Solving
-4 + n = 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 + n = 0 + 4

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

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

Simplifying
n = 4
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {4, 3}