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Simplifying 4n3 + -180n2 + -784n = 0 Reorder the terms: -784n + -180n2 + 4n3 = 0 Solving -784n + -180n2 + 4n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4n'. 4n(-196 + -45n + n2) = 0 Factor a trinomial. 4n((-4 + -1n)(49 + -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 '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 3
Set the factor '(49 + -1n)' equal to zero and attempt to solve: Simplifying 49 + -1n = 0 Solving 49 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + -1n = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -1n = 0 + -49 -1n = 0 + -49 Combine like terms: 0 + -49 = -49 -1n = -49 Divide each side by '-1'. n = 49 Simplifying n = 49Solution
n = {0, -4, 49}
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