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Simplifying 3n2 + 9n + -1512 = 0 Reorder the terms: -1512 + 9n + 3n2 = 0 Solving -1512 + 9n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-504 + 3n + n2) = 0 Factor a trinomial. 3((-24 + -1n)(21 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + -1n)' equal to zero and attempt to solve: Simplifying -24 + -1n = 0 Solving -24 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1n = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1n = 0 + 24 -1n = 0 + 24 Combine like terms: 0 + 24 = 24 -1n = 24 Divide each side by '-1'. n = -24 Simplifying n = -24Subproblem 2
Set the factor '(21 + -1n)' equal to zero and attempt to solve: Simplifying 21 + -1n = 0 Solving 21 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1n = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1n = 0 + -21 -1n = 0 + -21 Combine like terms: 0 + -21 = -21 -1n = -21 Divide each side by '-1'. n = 21 Simplifying n = 21Solution
n = {-24, 21}
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