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Simplifying 0 = -15n2 + 615n + -600 Reorder the terms: 0 = -600 + 615n + -15n2 Solving 0 = -600 + 615n + -15n2 Solving for variable 'n'. Combine like terms: 0 + 600 = 600 600 + -615n + 15n2 = -600 + 615n + -15n2 + 600 + -615n + 15n2 Reorder the terms: 600 + -615n + 15n2 = -600 + 600 + 615n + -615n + -15n2 + 15n2 Combine like terms: -600 + 600 = 0 600 + -615n + 15n2 = 0 + 615n + -615n + -15n2 + 15n2 600 + -615n + 15n2 = 615n + -615n + -15n2 + 15n2 Combine like terms: 615n + -615n = 0 600 + -615n + 15n2 = 0 + -15n2 + 15n2 600 + -615n + 15n2 = -15n2 + 15n2 Combine like terms: -15n2 + 15n2 = 0 600 + -615n + 15n2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(40 + -41n + n2) = 0 Factor a trinomial. 15((1 + -1n)(40 + -1n)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 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 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Subproblem 2
Set the factor '(40 + -1n)' equal to zero and attempt to solve: Simplifying 40 + -1n = 0 Solving 40 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1n = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1n = 0 + -40 -1n = 0 + -40 Combine like terms: 0 + -40 = -40 -1n = -40 Divide each side by '-1'. n = 40 Simplifying n = 40Solution
n = {1, 40}
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