(3n+6)(3n-5)=

Solution for (3n+6)(3n-5)= equation:

Simplifying
(3n + 6)(3n + -5) = 0

Reorder the terms:
(6 + 3n)(3n + -5) = 0

Reorder the terms:
(6 + 3n)(-5 + 3n) = 0

Multiply (6 + 3n) * (-5 + 3n)
(6(-5 + 3n) + 3n * (-5 + 3n)) = 0
((-5 * 6 + 3n * 6) + 3n * (-5 + 3n)) = 0
((-30 + 18n) + 3n * (-5 + 3n)) = 0
(-30 + 18n + (-5 * 3n + 3n * 3n)) = 0
(-30 + 18n + (-15n + 9n2)) = 0

Combine like terms: 18n + -15n = 3n
(-30 + 3n + 9n2) = 0

Solving
-30 + 3n + 9n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + n + 3n2) = 0

Factor a trinomial.
3((-2 + -1n)(5 + -3n)) = 0

Ignore the factor 3.
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 '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-2, 1.666666667}