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Simplifying (7n + -35)(5n + -4) = 0 Reorder the terms: (-35 + 7n)(5n + -4) = 0 Reorder the terms: (-35 + 7n)(-4 + 5n) = 0 Multiply (-35 + 7n) * (-4 + 5n) (-35(-4 + 5n) + 7n * (-4 + 5n)) = 0 ((-4 * -35 + 5n * -35) + 7n * (-4 + 5n)) = 0 ((140 + -175n) + 7n * (-4 + 5n)) = 0 (140 + -175n + (-4 * 7n + 5n * 7n)) = 0 (140 + -175n + (-28n + 35n2)) = 0 Combine like terms: -175n + -28n = -203n (140 + -203n + 35n2) = 0 Solving 140 + -203n + 35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7'. 7(20 + -29n + 5n2) = 0 Factor a trinomial. 7((4 + -5n)(5 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve: Simplifying 4 + -5n = 0 Solving 4 + -5n = 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 + -5n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5n = 0 + -4 -5n = 0 + -4 Combine like terms: 0 + -4 = -4 -5n = -4 Divide each side by '-5'. n = 0.8 Simplifying n = 0.8Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve: Simplifying 5 + -1n = 0 Solving 5 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1n = 0 + -5 -1n = 0 + -5 Combine like terms: 0 + -5 = -5 -1n = -5 Divide each side by '-1'. n = 5 Simplifying n = 5Solution
n = {0.8, 5}
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