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Simplifying (f + 8)(f + -2) = 0 Reorder the terms: (8 + f)(f + -2) = 0 Reorder the terms: (8 + f)(-2 + f) = 0 Multiply (8 + f) * (-2 + f) (8(-2 + f) + f(-2 + f)) = 0 ((-2 * 8 + f * 8) + f(-2 + f)) = 0 ((-16 + 8f) + f(-2 + f)) = 0 (-16 + 8f + (-2 * f + f * f)) = 0 (-16 + 8f + (-2f + f2)) = 0 Combine like terms: 8f + -2f = 6f (-16 + 6f + f2) = 0 Solving -16 + 6f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (-8 + -1f)(2 + -1f) = 0Subproblem 1
Set the factor '(-8 + -1f)' equal to zero and attempt to solve: Simplifying -8 + -1f = 0 Solving -8 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1f = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1f = 0 + 8 -1f = 0 + 8 Combine like terms: 0 + 8 = 8 -1f = 8 Divide each side by '-1'. f = -8 Simplifying f = -8Subproblem 2
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 = 2Solution
f = {-8, 2}
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