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Simplifying (3n + 5)(3n + -3) = 0 Reorder the terms: (5 + 3n)(3n + -3) = 0 Reorder the terms: (5 + 3n)(-3 + 3n) = 0 Multiply (5 + 3n) * (-3 + 3n) (5(-3 + 3n) + 3n * (-3 + 3n)) = 0 ((-3 * 5 + 3n * 5) + 3n * (-3 + 3n)) = 0 ((-15 + 15n) + 3n * (-3 + 3n)) = 0 (-15 + 15n + (-3 * 3n + 3n * 3n)) = 0 (-15 + 15n + (-9n + 9n2)) = 0 Combine like terms: 15n + -9n = 6n (-15 + 6n + 9n2) = 0 Solving -15 + 6n + 9n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 2n + 3n2) = 0 Factor a trinomial. 3((-5 + -3n)(1 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve: Simplifying -5 + -3n = 0 Solving -5 + -3n = 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 + -3n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3n = 0 + 5 -3n = 0 + 5 Combine like terms: 0 + 5 = 5 -3n = 5 Divide each side by '-3'. n = -1.666666667 Simplifying n = -1.666666667Subproblem 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 = {-1.666666667, 1}
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