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Simplifying (n + 2)(7n + -4) = 0 Reorder the terms: (2 + n)(7n + -4) = 0 Reorder the terms: (2 + n)(-4 + 7n) = 0 Multiply (2 + n) * (-4 + 7n) (2(-4 + 7n) + n(-4 + 7n)) = 0 ((-4 * 2 + 7n * 2) + n(-4 + 7n)) = 0 ((-8 + 14n) + n(-4 + 7n)) = 0 (-8 + 14n + (-4 * n + 7n * n)) = 0 (-8 + 14n + (-4n + 7n2)) = 0 Combine like terms: 14n + -4n = 10n (-8 + 10n + 7n2) = 0 Solving -8 + 10n + 7n2 = 0 Solving for variable 'n'. Factor a trinomial. (-2 + -1n)(4 + -7n) = 0Subproblem 1
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 = -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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