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Simplifying 12n(n + -4) + -5n = 10n + -3n Reorder the terms: 12n(-4 + n) + -5n = 10n + -3n (-4 * 12n + n * 12n) + -5n = 10n + -3n (-48n + 12n2) + -5n = 10n + -3n Reorder the terms: -48n + -5n + 12n2 = 10n + -3n Combine like terms: -48n + -5n = -53n -53n + 12n2 = 10n + -3n Combine like terms: 10n + -3n = 7n -53n + 12n2 = 7n Solving -53n + 12n2 = 7n Solving for variable 'n'. Reorder the terms: -53n + -7n + 12n2 = 7n + -7n Combine like terms: -53n + -7n = -60n -60n + 12n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -60n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '12n'. 12n(-5 + n) = 0 Ignore the factor 12.Subproblem 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 '(-5 + n)' equal to zero and attempt to solve: Simplifying -5 + n = 0 Solving -5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + n = 0 + 5 n = 0 + 5 Combine like terms: 0 + 5 = 5 n = 5 Simplifying n = 5Solution
n = {0, 5}
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