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Simplifying 15n2 + -162n + 243 = 0 Reorder the terms: 243 + -162n + 15n2 = 0 Solving 243 + -162n + 15n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(81 + -54n + 5n2) = 0 Factor a trinomial. 3((9 + -5n)(9 + -1n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -5n)' equal to zero and attempt to solve: Simplifying 9 + -5n = 0 Solving 9 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5n = 0 + -9 -5n = 0 + -9 Combine like terms: 0 + -9 = -9 -5n = -9 Divide each side by '-5'. n = 1.8 Simplifying n = 1.8Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {1.8, 9}
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