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Simplifying (3f + 5)(9f + 4) = 0 Reorder the terms: (5 + 3f)(9f + 4) = 0 Reorder the terms: (5 + 3f)(4 + 9f) = 0 Multiply (5 + 3f) * (4 + 9f) (5(4 + 9f) + 3f * (4 + 9f)) = 0 ((4 * 5 + 9f * 5) + 3f * (4 + 9f)) = 0 ((20 + 45f) + 3f * (4 + 9f)) = 0 (20 + 45f + (4 * 3f + 9f * 3f)) = 0 (20 + 45f + (12f + 27f2)) = 0 Combine like terms: 45f + 12f = 57f (20 + 57f + 27f2) = 0 Solving 20 + 57f + 27f2 = 0 Solving for variable 'f'. Factor a trinomial. (5 + 3f)(4 + 9f) = 0Subproblem 1
Set the factor '(5 + 3f)' equal to zero and attempt to solve: Simplifying 5 + 3f = 0 Solving 5 + 3f = 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 + 3f = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3f = 0 + -5 3f = 0 + -5 Combine like terms: 0 + -5 = -5 3f = -5 Divide each side by '3'. f = -1.666666667 Simplifying f = -1.666666667Subproblem 2
Set the factor '(4 + 9f)' equal to zero and attempt to solve: Simplifying 4 + 9f = 0 Solving 4 + 9f = 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 + 9f = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9f = 0 + -4 9f = 0 + -4 Combine like terms: 0 + -4 = -4 9f = -4 Divide each side by '9'. f = -0.4444444444 Simplifying f = -0.4444444444Solution
f = {-1.666666667, -0.4444444444}
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