6n^2=60-9n

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Solution for 6n^2=60-9n equation:


Simplifying
6n2 = 60 + -9n

Solving
6n2 = 60 + -9n

Solving for variable 'n'.

Reorder the terms:
-60 + 9n + 6n2 = 60 + -9n + -60 + 9n

Reorder the terms:
-60 + 9n + 6n2 = 60 + -60 + -9n + 9n

Combine like terms: 60 + -60 = 0
-60 + 9n + 6n2 = 0 + -9n + 9n
-60 + 9n + 6n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
-60 + 9n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + 3n + 2n2) = 0

Factor a trinomial.
3((-4 + -1n)(5 + -2n)) = 0

Ignore the factor 3.

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 '(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 = {-4, 2.5}

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