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Simplifying 9n4 + -19n3 + -24n2 = 0 Reorder the terms: -24n2 + -19n3 + 9n4 = 0 Solving -24n2 + -19n3 + 9n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n2'. n2(-24 + -19n + 9n2) = 0 Factor a trinomial. n2((-8 + -9n)(3 + -1n)) = 0Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(-8 + -9n)' equal to zero and attempt to solve: Simplifying -8 + -9n = 0 Solving -8 + -9n = 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 + -9n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9n = 0 + 8 -9n = 0 + 8 Combine like terms: 0 + 8 = 8 -9n = 8 Divide each side by '-9'. n = -0.8888888889 Simplifying n = -0.8888888889Subproblem 3
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {0, -0.8888888889, 3}
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