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Simplifying 63n2 + -132n + 45 = 0 Reorder the terms: 45 + -132n + 63n2 = 0 Solving 45 + -132n + 63n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -44n + 21n2) = 0 Factor a trinomial. 3((3 + -7n)(5 + -3n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -7n)' equal to zero and attempt to solve: Simplifying 3 + -7n = 0 Solving 3 + -7n = 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 + -7n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7n = 0 + -3 -7n = 0 + -3 Combine like terms: 0 + -3 = -3 -7n = -3 Divide each side by '-7'. n = 0.4285714286 Simplifying n = 0.4285714286Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {0.4285714286, 1.666666667}
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