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Simplifying 12f2 + -27f + 15 = 0 Reorder the terms: 15 + -27f + 12f2 = 0 Solving 15 + -27f + 12f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -9f + 4f2) = 0 Factor a trinomial. 3((1 + -1f)(5 + -4f)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1f)' equal to zero and attempt to solve: Simplifying 1 + -1f = 0 Solving 1 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1f = 0 + -1 -1f = 0 + -1 Combine like terms: 0 + -1 = -1 -1f = -1 Divide each side by '-1'. f = 1 Simplifying f = 1Subproblem 2
Set the factor '(5 + -4f)' equal to zero and attempt to solve: Simplifying 5 + -4f = 0 Solving 5 + -4f = 0 Move all terms containing f to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4f = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4f = 0 + -5 -4f = 0 + -5 Combine like terms: 0 + -5 = -5 -4f = -5 Divide each side by '-4'. f = 1.25 Simplifying f = 1.25Solution
f = {1, 1.25}
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