n(6n+12)=594

Solution for n(6n+12)=594 equation:

Simplifying
n(6n + 12) = 594

Reorder the terms:
n(12 + 6n) = 594
(12 * n + 6n * n) = 594
(12n + 6n2) = 594

Solving
12n + 6n2 = 594

Solving for variable 'n'.

Reorder the terms:
-594 + 12n + 6n2 = 594 + -594

Combine like terms: 594 + -594 = 0
-594 + 12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-99 + 2n + n2) = 0

Factor a trinomial.
6((-11 + -1n)(9 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve:

Simplifying
-11 + -1n = 0

Solving
-11 + -1n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1n = 0 + 11
-1n = 0 + 11

Combine like terms: 0 + 11 = 11
-1n = 11

Divide each side by '-1'.
n = -11

Simplifying
n = -11
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-11, 9}