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Simplifying 12f3 + -14f2 + -40f = 0 Reorder the terms: -40f + -14f2 + 12f3 = 0 Solving -40f + -14f2 + 12f3 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2f'. 2f(-20 + -7f + 6f2) = 0 Factor a trinomial. 2f((-4 + -3f)(5 + -2f)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'f' equal to zero and attempt to solve: Simplifying f = 0 Solving f = 0 Move all terms containing f to the left, all other terms to the right. Simplifying f = 0Subproblem 2
Set the factor '(-4 + -3f)' equal to zero and attempt to solve: Simplifying -4 + -3f = 0 Solving -4 + -3f = 0 Move all terms containing f to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3f = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3f = 0 + 4 -3f = 0 + 4 Combine like terms: 0 + 4 = 4 -3f = 4 Divide each side by '-3'. f = -1.333333333 Simplifying f = -1.333333333Subproblem 3
Set the factor '(5 + -2f)' equal to zero and attempt to solve: Simplifying 5 + -2f = 0 Solving 5 + -2f = 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 + -2f = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2f = 0 + -5 -2f = 0 + -5 Combine like terms: 0 + -5 = -5 -2f = -5 Divide each side by '-2'. f = 2.5 Simplifying f = 2.5Solution
f = {0, -1.333333333, 2.5}
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