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Simplifying -2n2(5n + -9 + 4n2) = 0 Reorder the terms: -2n2(-9 + 5n + 4n2) = 0 (-9 * -2n2 + 5n * -2n2 + 4n2 * -2n2) = 0 (18n2 + -10n3 + -8n4) = 0 Solving 18n2 + -10n3 + -8n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n2'. 2n2(9 + -5n + -4n2) = 0 Factor a trinomial. 2n2((1 + -1n)(9 + 4n)) = 0 Ignore the factor 2.Subproblem 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 '(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 '(9 + 4n)' equal to zero and attempt to solve: Simplifying 9 + 4n = 0 Solving 9 + 4n = 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 + 4n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4n = 0 + -9 4n = 0 + -9 Combine like terms: 0 + -9 = -9 4n = -9 Divide each side by '4'. n = -2.25 Simplifying n = -2.25Solution
n = {0, 1, -2.25}
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