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Simplifying (-8n + -8)(-4n + -6) = 0 Reorder the terms: (-8 + -8n)(-4n + -6) = 0 Reorder the terms: (-8 + -8n)(-6 + -4n) = 0 Multiply (-8 + -8n) * (-6 + -4n) (-8(-6 + -4n) + -8n * (-6 + -4n)) = 0 ((-6 * -8 + -4n * -8) + -8n * (-6 + -4n)) = 0 ((48 + 32n) + -8n * (-6 + -4n)) = 0 (48 + 32n + (-6 * -8n + -4n * -8n)) = 0 (48 + 32n + (48n + 32n2)) = 0 Combine like terms: 32n + 48n = 80n (48 + 80n + 32n2) = 0 Solving 48 + 80n + 32n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '16'. 16(3 + 5n + 2n2) = 0 Factor a trinomial. 16((3 + 2n)(1 + n)) = 0 Ignore the factor 16.Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1Solution
n = {-1.5, -1}
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