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Simplifying (7n + 4)(n + 2) = 0 Reorder the terms: (4 + 7n)(n + 2) = 0 Reorder the terms: (4 + 7n)(2 + n) = 0 Multiply (4 + 7n) * (2 + n) (4(2 + n) + 7n * (2 + n)) = 0 ((2 * 4 + n * 4) + 7n * (2 + n)) = 0 ((8 + 4n) + 7n * (2 + n)) = 0 (8 + 4n + (2 * 7n + n * 7n)) = 0 (8 + 4n + (14n + 7n2)) = 0 Combine like terms: 4n + 14n = 18n (8 + 18n + 7n2) = 0 Solving 8 + 18n + 7n2 = 0 Solving for variable 'n'. Factor a trinomial. (2 + n)(4 + 7n) = 0Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
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 = -0.5714285714Solution
n = {-2, -0.5714285714}
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