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Simplifying 40f2 + 65f + -30 = 0 Reorder the terms: -30 + 65f + 40f2 = 0 Solving -30 + 65f + 40f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 13f + 8f2) = 0 Factor a trinomial. 5((-2 + -1f)(3 + -8f)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1f)' equal to zero and attempt to solve: Simplifying -2 + -1f = 0 Solving -2 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1f = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1f = 0 + 2 -1f = 0 + 2 Combine like terms: 0 + 2 = 2 -1f = 2 Divide each side by '-1'. f = -2 Simplifying f = -2Subproblem 2
Set the factor '(3 + -8f)' equal to zero and attempt to solve: Simplifying 3 + -8f = 0 Solving 3 + -8f = 0 Move all terms containing f to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8f = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8f = 0 + -3 -8f = 0 + -3 Combine like terms: 0 + -3 = -3 -8f = -3 Divide each side by '-8'. f = 0.375 Simplifying f = 0.375Solution
f = {-2, 0.375}
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