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Simplifying (6n + 3)(6n + -4) = 0 Reorder the terms: (3 + 6n)(6n + -4) = 0 Reorder the terms: (3 + 6n)(-4 + 6n) = 0 Multiply (3 + 6n) * (-4 + 6n) (3(-4 + 6n) + 6n * (-4 + 6n)) = 0 ((-4 * 3 + 6n * 3) + 6n * (-4 + 6n)) = 0 ((-12 + 18n) + 6n * (-4 + 6n)) = 0 (-12 + 18n + (-4 * 6n + 6n * 6n)) = 0 (-12 + 18n + (-24n + 36n2)) = 0 Combine like terms: 18n + -24n = -6n (-12 + -6n + 36n2) = 0 Solving -12 + -6n + 36n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + -1n + 6n2) = 0 Factor a trinomial. 6((-1 + -2n)(2 + -3n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -2n)' equal to zero and attempt to solve: Simplifying -1 + -2n = 0 Solving -1 + -2n = 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 + -2n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2n = 0 + 1 -2n = 0 + 1 Combine like terms: 0 + 1 = 1 -2n = 1 Divide each side by '-2'. n = -0.5 Simplifying n = -0.5Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Solution
n = {-0.5, 0.6666666667}
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