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Simplifying -4n(n + -3) = 2(6 + -5n) + 12 Reorder the terms: -4n(-3 + n) = 2(6 + -5n) + 12 (-3 * -4n + n * -4n) = 2(6 + -5n) + 12 (12n + -4n2) = 2(6 + -5n) + 12 12n + -4n2 = (6 * 2 + -5n * 2) + 12 12n + -4n2 = (12 + -10n) + 12 Reorder the terms: 12n + -4n2 = 12 + 12 + -10n Combine like terms: 12 + 12 = 24 12n + -4n2 = 24 + -10n Solving 12n + -4n2 = 24 + -10n Solving for variable 'n'. Reorder the terms: -24 + 12n + 10n + -4n2 = 24 + -10n + -24 + 10n Combine like terms: 12n + 10n = 22n -24 + 22n + -4n2 = 24 + -10n + -24 + 10n Reorder the terms: -24 + 22n + -4n2 = 24 + -24 + -10n + 10n Combine like terms: 24 + -24 = 0 -24 + 22n + -4n2 = 0 + -10n + 10n -24 + 22n + -4n2 = -10n + 10n Combine like terms: -10n + 10n = 0 -24 + 22n + -4n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 11n + -2n2) = 0 Factor a trinomial. 2((-4 + n)(3 + -2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + n)' equal to zero and attempt to solve: Simplifying -4 + n = 0 Solving -4 + n = 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 + n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + n = 0 + 4 n = 0 + 4 Combine like terms: 0 + 4 = 4 n = 4 Simplifying n = 4Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {4, 1.5}
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