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Simplifying 2n4 + 3n3 + -27n2 = 0 Reorder the terms: -27n2 + 3n3 + 2n4 = 0 Solving -27n2 + 3n3 + 2n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n2'. n2(-27 + 3n + 2n2) = 0 Factor a trinomial. n2((-9 + -2n)(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 '(-9 + -2n)' equal to zero and attempt to solve: Simplifying -9 + -2n = 0 Solving -9 + -2n = 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 + -2n = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2n = 0 + 9 -2n = 0 + 9 Combine like terms: 0 + 9 = 9 -2n = 9 Divide each side by '-2'. n = -4.5 Simplifying n = -4.5Subproblem 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, -4.5, 3}
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