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Simplifying 3(n + -4)(n + 7) = 0 Reorder the terms: 3(-4 + n)(n + 7) = 0 Reorder the terms: 3(-4 + n)(7 + n) = 0 Multiply (-4 + n) * (7 + n) 3(-4(7 + n) + n(7 + n)) = 0 3((7 * -4 + n * -4) + n(7 + n)) = 0 3((-28 + -4n) + n(7 + n)) = 0 3(-28 + -4n + (7 * n + n * n)) = 0 3(-28 + -4n + (7n + n2)) = 0 Combine like terms: -4n + 7n = 3n 3(-28 + 3n + n2) = 0 (-28 * 3 + 3n * 3 + n2 * 3) = 0 (-84 + 9n + 3n2) = 0 Solving -84 + 9n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + 3n + n2) = 0 Factor a trinomial. 3((-7 + -1n)(4 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 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 = 4Solution
n = {-7, 4}
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