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Simplifying 4n(3n2 + 6n + -9) = 0 Reorder the terms: 4n(-9 + 6n + 3n2) = 0 (-9 * 4n + 6n * 4n + 3n2 * 4n) = 0 (-36n + 24n2 + 12n3) = 0 Solving -36n + 24n2 + 12n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '12n'. 12n(-3 + 2n + n2) = 0 Factor a trinomial. 12n((-3 + -1n)(1 + -1n)) = 0 Ignore the factor 12.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 '(-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 = -3Subproblem 3
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 = 1Solution
n = {0, -3, 1}
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