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Simplifying (2n + -3) * 5n + -1(2n + -3)(n + -2) = 0 Reorder the terms: (-3 + 2n) * 5n + -1(2n + -3)(n + -2) = 0 Reorder the terms for easier multiplication: 5n(-3 + 2n) + -1(2n + -3)(n + -2) = 0 (-3 * 5n + 2n * 5n) + -1(2n + -3)(n + -2) = 0 (-15n + 10n2) + -1(2n + -3)(n + -2) = 0 Reorder the terms: -15n + 10n2 + -1(-3 + 2n)(n + -2) = 0 Reorder the terms: -15n + 10n2 + -1(-3 + 2n)(-2 + n) = 0 Multiply (-3 + 2n) * (-2 + n) -15n + 10n2 + -1(-3(-2 + n) + 2n * (-2 + n)) = 0 -15n + 10n2 + -1((-2 * -3 + n * -3) + 2n * (-2 + n)) = 0 -15n + 10n2 + -1((6 + -3n) + 2n * (-2 + n)) = 0 -15n + 10n2 + -1(6 + -3n + (-2 * 2n + n * 2n)) = 0 -15n + 10n2 + -1(6 + -3n + (-4n + 2n2)) = 0 Combine like terms: -3n + -4n = -7n -15n + 10n2 + -1(6 + -7n + 2n2) = 0 -15n + 10n2 + (6 * -1 + -7n * -1 + 2n2 * -1) = 0 -15n + 10n2 + (-6 + 7n + -2n2) = 0 Reorder the terms: -6 + -15n + 7n + 10n2 + -2n2 = 0 Combine like terms: -15n + 7n = -8n -6 + -8n + 10n2 + -2n2 = 0 Combine like terms: 10n2 + -2n2 = 8n2 -6 + -8n + 8n2 = 0 Solving -6 + -8n + 8n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -4n + 4n2) = 0 Factor a trinomial. 2((-1 + -2n)(3 + -2n)) = 0 Ignore the factor 2.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 '(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 = {-0.5, 1.5}
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