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

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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}

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