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Simplifying 42n2 + -396n + 480 = 0 Reorder the terms: 480 + -396n + 42n2 = 0 Solving 480 + -396n + 42n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(80 + -66n + 7n2) = 0 Factor a trinomial. 6((10 + -7n)(8 + -1n)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(10 + -7n)' equal to zero and attempt to solve: Simplifying 10 + -7n = 0 Solving 10 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -7n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7n = 0 + -10 -7n = 0 + -10 Combine like terms: 0 + -10 = -10 -7n = -10 Divide each side by '-7'. n = 1.428571429 Simplifying n = 1.428571429Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {1.428571429, 8}
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