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Simplifying 6n2 = 30n + 84 Reorder the terms: 6n2 = 84 + 30n Solving 6n2 = 84 + 30n Solving for variable 'n'. Reorder the terms: -84 + -30n + 6n2 = 84 + 30n + -84 + -30n Reorder the terms: -84 + -30n + 6n2 = 84 + -84 + 30n + -30n Combine like terms: 84 + -84 = 0 -84 + -30n + 6n2 = 0 + 30n + -30n -84 + -30n + 6n2 = 30n + -30n Combine like terms: 30n + -30n = 0 -84 + -30n + 6n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-14 + -5n + n2) = 0 Factor a trinomial. 6((-2 + -1n)(7 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Divide each side by '-1'. n = 7 Simplifying n = 7Solution
n = {-2, 7}
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