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Simplifying (f + 2)(3f + 7) = 0 Reorder the terms: (2 + f)(3f + 7) = 0 Reorder the terms: (2 + f)(7 + 3f) = 0 Multiply (2 + f) * (7 + 3f) (2(7 + 3f) + f(7 + 3f)) = 0 ((7 * 2 + 3f * 2) + f(7 + 3f)) = 0 ((14 + 6f) + f(7 + 3f)) = 0 (14 + 6f + (7 * f + 3f * f)) = 0 (14 + 6f + (7f + 3f2)) = 0 Combine like terms: 6f + 7f = 13f (14 + 13f + 3f2) = 0 Solving 14 + 13f + 3f2 = 0 Solving for variable 'f'. Factor a trinomial. (7 + 3f)(2 + f) = 0Subproblem 1
Set the factor '(7 + 3f)' equal to zero and attempt to solve: Simplifying 7 + 3f = 0 Solving 7 + 3f = 0 Move all terms containing f to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3f = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3f = 0 + -7 3f = 0 + -7 Combine like terms: 0 + -7 = -7 3f = -7 Divide each side by '3'. f = -2.333333333 Simplifying f = -2.333333333Subproblem 2
Set the factor '(2 + f)' equal to zero and attempt to solve: Simplifying 2 + f = 0 Solving 2 + f = 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 + f = 0 + -2 Combine like terms: 2 + -2 = 0 0 + f = 0 + -2 f = 0 + -2 Combine like terms: 0 + -2 = -2 f = -2 Simplifying f = -2Solution
f = {-2.333333333, -2}
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