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Simplifying n(n + -6) + -12(n + -6) = 0 Reorder the terms: n(-6 + n) + -12(n + -6) = 0 (-6 * n + n * n) + -12(n + -6) = 0 (-6n + n2) + -12(n + -6) = 0 Reorder the terms: -6n + n2 + -12(-6 + n) = 0 -6n + n2 + (-6 * -12 + n * -12) = 0 -6n + n2 + (72 + -12n) = 0 Reorder the terms: 72 + -6n + -12n + n2 = 0 Combine like terms: -6n + -12n = -18n 72 + -18n + n2 = 0 Solving 72 + -18n + n2 = 0 Solving for variable 'n'. Factor a trinomial. (6 + -1n)(12 + -1n) = 0Subproblem 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 '(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 = {6, 12}
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