(3n-9)(2n+5)=0

Solution for (3n-9)(2n+5)=0 equation:

Simplifying
(3n + -9)(2n + 5) = 0

Reorder the terms:
(-9 + 3n)(2n + 5) = 0

Reorder the terms:
(-9 + 3n)(5 + 2n) = 0

Multiply (-9 + 3n) * (5 + 2n)
(-9(5 + 2n) + 3n * (5 + 2n)) = 0
((5 * -9 + 2n * -9) + 3n * (5 + 2n)) = 0
((-45 + -18n) + 3n * (5 + 2n)) = 0
(-45 + -18n + (5 * 3n + 2n * 3n)) = 0
(-45 + -18n + (15n + 6n2)) = 0

Combine like terms: -18n + 15n = -3n
(-45 + -3n + 6n2) = 0

Solving
-45 + -3n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -1n + 2n2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 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 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
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 = {-2.5, 3}