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Simplifying 3n2 = -3n + 90 Reorder the terms: 3n2 = 90 + -3n Solving 3n2 = 90 + -3n Solving for variable 'n'. Reorder the terms: -90 + 3n + 3n2 = 90 + -3n + -90 + 3n Reorder the terms: -90 + 3n + 3n2 = 90 + -90 + -3n + 3n Combine like terms: 90 + -90 = 0 -90 + 3n + 3n2 = 0 + -3n + 3n -90 + 3n + 3n2 = -3n + 3n Combine like terms: -3n + 3n = 0 -90 + 3n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-30 + n + n2) = 0 Factor a trinomial. 3((-6 + -1n)(5 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
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 = 5Solution
n = {-6, 5}
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