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Simplifying 0 = (3f + 5)(2f + 5) Reorder the terms: 0 = (5 + 3f)(2f + 5) Reorder the terms: 0 = (5 + 3f)(5 + 2f) Multiply (5 + 3f) * (5 + 2f) 0 = (5(5 + 2f) + 3f * (5 + 2f)) 0 = ((5 * 5 + 2f * 5) + 3f * (5 + 2f)) 0 = ((25 + 10f) + 3f * (5 + 2f)) 0 = (25 + 10f + (5 * 3f + 2f * 3f)) 0 = (25 + 10f + (15f + 6f2)) Combine like terms: 10f + 15f = 25f 0 = (25 + 25f + 6f2) Solving 0 = 25 + 25f + 6f2 Solving for variable 'f'. Combine like terms: 0 + -25 = -25 -25 + -25f + -6f2 = 25 + 25f + 6f2 + -25 + -25f + -6f2 Reorder the terms: -25 + -25f + -6f2 = 25 + -25 + 25f + -25f + 6f2 + -6f2 Combine like terms: 25 + -25 = 0 -25 + -25f + -6f2 = 0 + 25f + -25f + 6f2 + -6f2 -25 + -25f + -6f2 = 25f + -25f + 6f2 + -6f2 Combine like terms: 25f + -25f = 0 -25 + -25f + -6f2 = 0 + 6f2 + -6f2 -25 + -25f + -6f2 = 6f2 + -6f2 Combine like terms: 6f2 + -6f2 = 0 -25 + -25f + -6f2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 25f + 6f2) = 0 Factor a trinomial. -1((5 + 2f)(5 + 3f)) = 0 Ignore the factor -1.Subproblem 1
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 = -2.5Subproblem 2
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 = -1.666666667Solution
f = {-2.5, -1.666666667}
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