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Simplifying (n + 8)(7n + -4) = 0 Reorder the terms: (8 + n)(7n + -4) = 0 Reorder the terms: (8 + n)(-4 + 7n) = 0 Multiply (8 + n) * (-4 + 7n) (8(-4 + 7n) + n(-4 + 7n)) = 0 ((-4 * 8 + 7n * 8) + n(-4 + 7n)) = 0 ((-32 + 56n) + n(-4 + 7n)) = 0 (-32 + 56n + (-4 * n + 7n * n)) = 0 (-32 + 56n + (-4n + 7n2)) = 0 Combine like terms: 56n + -4n = 52n (-32 + 52n + 7n2) = 0 Solving -32 + 52n + 7n2 = 0 Solving for variable 'n'. Factor a trinomial. (-8 + -1n)(4 + -7n) = 0Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve: Simplifying -8 + -1n = 0 Solving -8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1n = 0 + 8 -1n = 0 + 8 Combine like terms: 0 + 8 = 8 -1n = 8 Divide each side by '-1'. n = -8 Simplifying n = -8Subproblem 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 = {-8, 0.5714285714}
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