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Simplifying (-4n + -6)(5n + -2) = 0 Reorder the terms: (-6 + -4n)(5n + -2) = 0 Reorder the terms: (-6 + -4n)(-2 + 5n) = 0 Multiply (-6 + -4n) * (-2 + 5n) (-6(-2 + 5n) + -4n * (-2 + 5n)) = 0 ((-2 * -6 + 5n * -6) + -4n * (-2 + 5n)) = 0 ((12 + -30n) + -4n * (-2 + 5n)) = 0 (12 + -30n + (-2 * -4n + 5n * -4n)) = 0 (12 + -30n + (8n + -20n2)) = 0 Combine like terms: -30n + 8n = -22n (12 + -22n + -20n2) = 0 Solving 12 + -22n + -20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -11n + -10n2) = 0 Factor a trinomial. 2((2 + -5n)(3 + 2n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5n)' equal to zero and attempt to solve: Simplifying 2 + -5n = 0 Solving 2 + -5n = 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 + -5n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n = 0 + -2 -5n = 0 + -2 Combine like terms: 0 + -2 = -2 -5n = -2 Divide each side by '-5'. n = 0.4 Simplifying n = 0.4Subproblem 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 = {0.4, -1.5}
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