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Simplifying 30n2 + -5n = 5 Reorder the terms: -5n + 30n2 = 5 Solving -5n + 30n2 = 5 Solving for variable 'n'. Reorder the terms: -5 + -5n + 30n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -5n + 30n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -1n + 6n2) = 0 Factor a trinomial. 5((-1 + -3n)(1 + -2n)) = 0 Ignore the factor 5.Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Solution
n = {-0.3333333333, 0.5}
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