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Simplifying 42n2 + 72 = 150n Reorder the terms: 72 + 42n2 = 150n Solving 72 + 42n2 = 150n Solving for variable 'n'. Reorder the terms: 72 + -150n + 42n2 = 150n + -150n Combine like terms: 150n + -150n = 0 72 + -150n + 42n2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(12 + -25n + 7n2) = 0 Factor a trinomial. 6((4 + -7n)(3 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -7n)' equal to zero and attempt to solve: Simplifying 4 + -7n = 0 Solving 4 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7n = 0 + -4 -7n = 0 + -4 Combine like terms: 0 + -4 = -4 -7n = -4 Divide each side by '-7'. n = 0.5714285714 Simplifying n = 0.5714285714Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Divide each side by '-1'. n = 3 Simplifying n = 3Solution
n = {0.5714285714, 3}
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