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Simplifying 35n2 + 165n + -50 = 0 Reorder the terms: -50 + 165n + 35n2 = 0 Solving -50 + 165n + 35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + 33n + 7n2) = 0 Factor a trinomial. 5((-5 + -1n)(2 + -7n)) = 0 Ignore the factor 5.Subproblem 1
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 = -5Subproblem 2
Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 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 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857Solution
n = {-5, 0.2857142857}
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