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Simplifying (2n + -5)(7n + 7) = 0 Reorder the terms: (-5 + 2n)(7n + 7) = 0 Reorder the terms: (-5 + 2n)(7 + 7n) = 0 Multiply (-5 + 2n) * (7 + 7n) (-5(7 + 7n) + 2n * (7 + 7n)) = 0 ((7 * -5 + 7n * -5) + 2n * (7 + 7n)) = 0 ((-35 + -35n) + 2n * (7 + 7n)) = 0 (-35 + -35n + (7 * 2n + 7n * 2n)) = 0 (-35 + -35n + (14n + 14n2)) = 0 Combine like terms: -35n + 14n = -21n (-35 + -21n + 14n2) = 0 Solving -35 + -21n + 14n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + -3n + 2n2) = 0 Factor a trinomial. 7((-1 + -1n)(5 + -2n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 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 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {-1, 2.5}
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