6r^2+54r+120=0

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Solution for 6r^2+54r+120=0 equation:


Simplifying
6r2 + 54r + 120 = 0

Reorder the terms:
120 + 54r + 6r2 = 0

Solving
120 + 54r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + 9r + r2) = 0

Factor a trinomial.
6((5 + r)(4 + r)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5

Subproblem 2

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

Solution

r = {-5, -4}

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