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Simplifying 30n2 + 294n + 216 = 0 Reorder the terms: 216 + 294n + 30n2 = 0 Solving 216 + 294n + 30n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(36 + 49n + 5n2) = 0 Factor a trinomial. 6((9 + n)(4 + 5n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve: Simplifying 9 + n = 0 Solving 9 + n = 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 + n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + n = 0 + -9 n = 0 + -9 Combine like terms: 0 + -9 = -9 n = -9 Simplifying n = -9Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve: Simplifying 4 + 5n = 0 Solving 4 + 5n = 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 + 5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5n = 0 + -4 5n = 0 + -4 Combine like terms: 0 + -4 = -4 5n = -4 Divide each side by '5'. n = -0.8 Simplifying n = -0.8Solution
n = {-9, -0.8}
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