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Simplifying (n + 6n + -4)(2n + -4) = 0 Reorder the terms: (-4 + n + 6n)(2n + -4) = 0 Combine like terms: n + 6n = 7n (-4 + 7n)(2n + -4) = 0 Reorder the terms: (-4 + 7n)(-4 + 2n) = 0 Multiply (-4 + 7n) * (-4 + 2n) (-4(-4 + 2n) + 7n * (-4 + 2n)) = 0 ((-4 * -4 + 2n * -4) + 7n * (-4 + 2n)) = 0 ((16 + -8n) + 7n * (-4 + 2n)) = 0 (16 + -8n + (-4 * 7n + 2n * 7n)) = 0 (16 + -8n + (-28n + 14n2)) = 0 Combine like terms: -8n + -28n = -36n (16 + -36n + 14n2) = 0 Solving 16 + -36n + 14n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -18n + 7n2) = 0 Factor a trinomial. 2((4 + -7n)(2 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -7n)' equal to zero and attempt to solve: Simplifying 4 + -7n = 0 Solving 4 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7n = 0 + -4 -7n = 0 + -4 Combine like terms: 0 + -4 = -4 -7n = -4 Divide each side by '-7'. n = 0.5714285714 Simplifying n = 0.5714285714Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 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 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {0.5714285714, 2}
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