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Simplifying (f + 7)(2f + -4) + -1(3f + 1) * 2 = 0 Reorder the terms: (7 + f)(2f + -4) + -1(3f + 1) * 2 = 0 Reorder the terms: (7 + f)(-4 + 2f) + -1(3f + 1) * 2 = 0 Multiply (7 + f) * (-4 + 2f) (7(-4 + 2f) + f(-4 + 2f)) + -1(3f + 1) * 2 = 0 ((-4 * 7 + 2f * 7) + f(-4 + 2f)) + -1(3f + 1) * 2 = 0 ((-28 + 14f) + f(-4 + 2f)) + -1(3f + 1) * 2 = 0 (-28 + 14f + (-4 * f + 2f * f)) + -1(3f + 1) * 2 = 0 (-28 + 14f + (-4f + 2f2)) + -1(3f + 1) * 2 = 0 Combine like terms: 14f + -4f = 10f (-28 + 10f + 2f2) + -1(3f + 1) * 2 = 0 Reorder the terms: -28 + 10f + 2f2 + -1(1 + 3f) * 2 = 0 Reorder the terms for easier multiplication: -28 + 10f + 2f2 + -1 * 2(1 + 3f) = 0 Multiply -1 * 2 -28 + 10f + 2f2 + -2(1 + 3f) = 0 -28 + 10f + 2f2 + (1 * -2 + 3f * -2) = 0 -28 + 10f + 2f2 + (-2 + -6f) = 0 Reorder the terms: -28 + -2 + 10f + -6f + 2f2 = 0 Combine like terms: -28 + -2 = -30 -30 + 10f + -6f + 2f2 = 0 Combine like terms: 10f + -6f = 4f -30 + 4f + 2f2 = 0 Solving -30 + 4f + 2f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 2f + f2) = 0 Factor a trinomial. 2((-5 + -1f)(3 + -1f)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1f)' equal to zero and attempt to solve: Simplifying -5 + -1f = 0 Solving -5 + -1f = 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 + -1f = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1f = 0 + 5 -1f = 0 + 5 Combine like terms: 0 + 5 = 5 -1f = 5 Divide each side by '-1'. f = -5 Simplifying f = -5Subproblem 2
Set the factor '(3 + -1f)' equal to zero and attempt to solve: Simplifying 3 + -1f = 0 Solving 3 + -1f = 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 + -1f = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1f = 0 + -3 -1f = 0 + -3 Combine like terms: 0 + -3 = -3 -1f = -3 Divide each side by '-1'. f = 3 Simplifying f = 3Solution
f = {-5, 3}
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