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Simplifying 30n2 + -192 = 216n Reorder the terms: -192 + 30n2 = 216n Solving -192 + 30n2 = 216n Solving for variable 'n'. Reorder the terms: -192 + -216n + 30n2 = 216n + -216n Combine like terms: 216n + -216n = 0 -192 + -216n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-32 + -36n + 5n2) = 0 Factor a trinomial. 6((-4 + -5n)(8 + -1n)) = 0 Ignore the factor 6.Subproblem 1
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 = -0.8Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-0.8, 8}
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