2(n-9)(n+6)=0

Solution for 2(n-9)(n+6)=0 equation:

Simplifying
2(n + -9)(n + 6) = 0

Reorder the terms:
2(-9 + n)(n + 6) = 0

Reorder the terms:
2(-9 + n)(6 + n) = 0

Multiply (-9 + n) * (6 + n)
2(-9(6 + n) + n(6 + n)) = 0
2((6 * -9 + n * -9) + n(6 + n)) = 0
2((-54 + -9n) + n(6 + n)) = 0
2(-54 + -9n + (6 * n + n * n)) = 0
2(-54 + -9n + (6n + n2)) = 0

Combine like terms: -9n + 6n = -3n
2(-54 + -3n + n2) = 0
(-54 * 2 + -3n * 2 + n2 * 2) = 0
(-108 + -6n + 2n2) = 0

Solving
-108 + -6n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3n + n2) = 0

Factor a trinomial.
2((-6 + -1n)(9 + -1n)) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
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 = {-6, 9}