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Simplifying 6n3 = 21n2 + -15n Reorder the terms: 6n3 = -15n + 21n2 Solving 6n3 = -15n + 21n2 Solving for variable 'n'. Reorder the terms: 15n + -21n2 + 6n3 = -15n + 21n2 + 15n + -21n2 Reorder the terms: 15n + -21n2 + 6n3 = -15n + 15n + 21n2 + -21n2 Combine like terms: -15n + 15n = 0 15n + -21n2 + 6n3 = 0 + 21n2 + -21n2 15n + -21n2 + 6n3 = 21n2 + -21n2 Combine like terms: 21n2 + -21n2 = 0 15n + -21n2 + 6n3 = 0 Factor out the Greatest Common Factor (GCF), '3n'. 3n(5 + -7n + 2n2) = 0 Factor a trinomial. 3n((1 + -1n)(5 + -2n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 3
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 = 2.5Solution
n = {0, 1, 2.5}
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