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Simplifying n(n + -6)(n + -12) = 0 Reorder the terms: n(-6 + n)(n + -12) = 0 Reorder the terms: n(-6 + n)(-12 + n) = 0 Multiply (-6 + n) * (-12 + n) n(-6(-12 + n) + n(-12 + n)) = 0 n((-12 * -6 + n * -6) + n(-12 + n)) = 0 n((72 + -6n) + n(-12 + n)) = 0 n(72 + -6n + (-12 * n + n * n)) = 0 n(72 + -6n + (-12n + n2)) = 0 Combine like terms: -6n + -12n = -18n n(72 + -18n + n2) = 0 (72 * n + -18n * n + n2 * n) = 0 (72n + -18n2 + n3) = 0 Solving 72n + -18n2 + n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(72 + -18n + n2) = 0 Factor a trinomial. n((6 + -1n)(12 + -1n)) = 0Subproblem 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 '(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 3
Set the factor '(12 + -1n)' equal to zero and attempt to solve: Simplifying 12 + -1n = 0 Solving 12 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12Solution
n = {0, 6, 12}
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