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Simplifying 4n3 + -12n2 + -1672n = 0 Reorder the terms: -1672n + -12n2 + 4n3 = 0 Solving -1672n + -12n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n'. 4n(-418 + -3n + n2) = 0 Factor a trinomial. 4n((-19 + -1n)(22 + -1n)) = 0 Ignore the factor 4.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 '(-19 + -1n)' equal to zero and attempt to solve: Simplifying -19 + -1n = 0 Solving -19 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1n = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1n = 0 + 19 -1n = 0 + 19 Combine like terms: 0 + 19 = 19 -1n = 19 Divide each side by '-1'. n = -19 Simplifying n = -19Subproblem 3
Set the factor '(22 + -1n)' equal to zero and attempt to solve: Simplifying 22 + -1n = 0 Solving 22 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -1n = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -1n = 0 + -22 -1n = 0 + -22 Combine like terms: 0 + -22 = -22 -1n = -22 Divide each side by '-1'. n = 22 Simplifying n = 22Solution
n = {0, -19, 22}
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