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Simplifying 28n2 + 44n + -120 = 0 Reorder the terms: -120 + 44n + 28n2 = 0 Solving -120 + 44n + 28n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + 11n + 7n2) = 0 Factor a trinomial. 4((-3 + -1n)(10 + -7n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(10 + -7n)' equal to zero and attempt to solve: Simplifying 10 + -7n = 0 Solving 10 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -7n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7n = 0 + -10 -7n = 0 + -10 Combine like terms: 0 + -10 = -10 -7n = -10 Divide each side by '-7'. n = 1.428571429 Simplifying n = 1.428571429Solution
n = {-3, 1.428571429}
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