-9n(n-12)=243

Solution for -9n(n-12)=243 equation:

Simplifying
-9n(n + -12) = 243

Reorder the terms:
-9n(-12 + n) = 243
(-12 * -9n + n * -9n) = 243
(108n + -9n2) = 243

Solving
108n + -9n2 = 243

Solving for variable 'n'.

Reorder the terms:
-243 + 108n + -9n2 = 243 + -243

Combine like terms: 243 + -243 = 0
-243 + 108n + -9n2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-27 + 12n + -1n2) = 0

Factor a trinomial.
9((-9 + n)(3 + -1n)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-9 + n)' equal to zero and attempt to solve:

Simplifying
-9 + n = 0

Solving
-9 + n = 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 + n = 0 + 9

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

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

Simplifying
n = 9
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 = {9, 3}