6n^2-30n-216=0

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Solution for 6n^2-30n-216=0 equation:


Simplifying
6n2 + -30n + -216 = 0

Reorder the terms:
-216 + -30n + 6n2 = 0

Solving
-216 + -30n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-36 + -5n + n2) = 0

Factor a trinomial.
6((-4 + -1n)(9 + -1n)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4

Subproblem 2

Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9

Solution

n = {-4, 9}

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