6n^2-12n-42=6

Solution for 6n^2-12n-42=6 equation:

Simplifying
6n2 + -12n + -42 = 6

Reorder the terms:
-42 + -12n + 6n2 = 6

Solving
-42 + -12n + 6n2 = 6

Solving for variable 'n'.

Reorder the terms:
-42 + -6 + -12n + 6n2 = 6 + -6

Combine like terms: -42 + -6 = -48
-48 + -12n + 6n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-48 + -12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -2n + n2) = 0

Factor a trinomial.
6((-2 + -1n)(4 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

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

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

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
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
Solution
n = {-2, 4}