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Simplifying (4n + 4)(5n + -8) = 0 Reorder the terms: (4 + 4n)(5n + -8) = 0 Reorder the terms: (4 + 4n)(-8 + 5n) = 0 Multiply (4 + 4n) * (-8 + 5n) (4(-8 + 5n) + 4n * (-8 + 5n)) = 0 ((-8 * 4 + 5n * 4) + 4n * (-8 + 5n)) = 0 ((-32 + 20n) + 4n * (-8 + 5n)) = 0 (-32 + 20n + (-8 * 4n + 5n * 4n)) = 0 (-32 + 20n + (-32n + 20n2)) = 0 Combine like terms: 20n + -32n = -12n (-32 + -12n + 20n2) = 0 Solving -32 + -12n + 20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + -3n + 5n2) = 0 Factor a trinomial. 4((-1 + -1n)(8 + -5n)) = 0 Ignore the factor 4.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 '(8 + -5n)' equal to zero and attempt to solve: Simplifying 8 + -5n = 0 Solving 8 + -5n = 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 + -5n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5n = 0 + -8 -5n = 0 + -8 Combine like terms: 0 + -8 = -8 -5n = -8 Divide each side by '-5'. n = 1.6 Simplifying n = 1.6Solution
n = {-1, 1.6}
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