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Simplifying 12n2 + -50n + 45 = 3 Reorder the terms: 45 + -50n + 12n2 = 3 Solving 45 + -50n + 12n2 = 3 Solving for variable 'n'. Reorder the terms: 45 + -3 + -50n + 12n2 = 3 + -3 Combine like terms: 45 + -3 = 42 42 + -50n + 12n2 = 3 + -3 Combine like terms: 3 + -3 = 0 42 + -50n + 12n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -25n + 6n2) = 0 Factor a trinomial. 2((7 + -6n)(3 + -1n)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -6n)' equal to zero and attempt to solve: Simplifying 7 + -6n = 0 Solving 7 + -6n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6n = 0 + -7 -6n = 0 + -7 Combine like terms: 0 + -7 = -7 -6n = -7 Divide each side by '-6'. n = 1.166666667 Simplifying n = 1.166666667Subproblem 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 = {1.166666667, 3}
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