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

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

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

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

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

Multiply (-5 + 2n) * (2 + n)
9(-5(2 + n) + 2n * (2 + n)) = 0
9((2 * -5 + n * -5) + 2n * (2 + n)) = 0
9((-10 + -5n) + 2n * (2 + n)) = 0
9(-10 + -5n + (2 * 2n + n * 2n)) = 0
9(-10 + -5n + (4n + 2n2)) = 0

Combine like terms: -5n + 4n = -1n
9(-10 + -1n + 2n2) = 0
(-10 * 9 + -1n * 9 + 2n2 * 9) = 0
(-90 + -9n + 18n2) = 0

Solving
-90 + -9n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-10 + -1n + 2n2) = 0

Factor a trinomial.
9((-2 + -1n)(5 + -2n)) = 0

Ignore the factor 9.
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 + -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
Solution
n = {-2, 2.5}