8(9n+27)(6n-9)=0

Solution for 8(9n+27)(6n-9)=0 equation:

Simplifying
8(9n + 27)(6n + -9) = 0

Reorder the terms:
8(27 + 9n)(6n + -9) = 0

Reorder the terms:
8(27 + 9n)(-9 + 6n) = 0

Multiply (27 + 9n) * (-9 + 6n)
8(27(-9 + 6n) + 9n * (-9 + 6n)) = 0
8((-9 * 27 + 6n * 27) + 9n * (-9 + 6n)) = 0
8((-243 + 162n) + 9n * (-9 + 6n)) = 0
8(-243 + 162n + (-9 * 9n + 6n * 9n)) = 0
8(-243 + 162n + (-81n + 54n2)) = 0

Combine like terms: 162n + -81n = 81n
8(-243 + 81n + 54n2) = 0
(-243 * 8 + 81n * 8 + 54n2 * 8) = 0
(-1944 + 648n + 432n2) = 0

Solving
-1944 + 648n + 432n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '216'.
216(-9 + 3n + 2n2) = 0

Factor a trinomial.
216((-3 + -1n)(3 + -2n)) = 0

Ignore the factor 216.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-3, 1.5}