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Simplifying 5(n + 6)(n + -1) = 0 Reorder the terms: 5(6 + n)(n + -1) = 0 Reorder the terms: 5(6 + n)(-1 + n) = 0 Multiply (6 + n) * (-1 + n) 5(6(-1 + n) + n(-1 + n)) = 0 5((-1 * 6 + n * 6) + n(-1 + n)) = 0 5((-6 + 6n) + n(-1 + n)) = 0 5(-6 + 6n + (-1 * n + n * n)) = 0 5(-6 + 6n + (-1n + n2)) = 0 Combine like terms: 6n + -1n = 5n 5(-6 + 5n + n2) = 0 (-6 * 5 + 5n * 5 + n2 * 5) = 0 (-30 + 25n + 5n2) = 0 Solving -30 + 25n + 5n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 5n + n2) = 0 Factor a trinomial. 5((-6 + -1n)(1 + -1n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
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 = {-6, 1}
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