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Simplifying 30n2 + -15 = -35n Reorder the terms: -15 + 30n2 = -35n Solving -15 + 30n2 = -35n Solving for variable 'n'. Reorder the terms: -15 + 35n + 30n2 = -35n + 35n Combine like terms: -35n + 35n = 0 -15 + 35n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 7n + 6n2) = 0 Factor a trinomial. 5((-3 + -2n)(1 + -3n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -2n)' equal to zero and attempt to solve: Simplifying -3 + -2n = 0 Solving -3 + -2n = 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 + -2n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2n = 0 + 3 -2n = 0 + 3 Combine like terms: 0 + 3 = 3 -2n = 3 Divide each side by '-2'. n = -1.5 Simplifying n = -1.5Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-1.5, 0.3333333333}
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