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Simplifying (f + -16)(f + -27) = 0 Reorder the terms: (-16 + f)(f + -27) = 0 Reorder the terms: (-16 + f)(-27 + f) = 0 Multiply (-16 + f) * (-27 + f) (-16(-27 + f) + f(-27 + f)) = 0 ((-27 * -16 + f * -16) + f(-27 + f)) = 0 ((432 + -16f) + f(-27 + f)) = 0 (432 + -16f + (-27 * f + f * f)) = 0 (432 + -16f + (-27f + f2)) = 0 Combine like terms: -16f + -27f = -43f (432 + -43f + f2) = 0 Solving 432 + -43f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (16 + -1f)(27 + -1f) = 0Subproblem 1
Set the factor '(16 + -1f)' equal to zero and attempt to solve: Simplifying 16 + -1f = 0 Solving 16 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1f = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1f = 0 + -16 -1f = 0 + -16 Combine like terms: 0 + -16 = -16 -1f = -16 Divide each side by '-1'. f = 16 Simplifying f = 16Subproblem 2
Set the factor '(27 + -1f)' equal to zero and attempt to solve: Simplifying 27 + -1f = 0 Solving 27 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1f = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1f = 0 + -27 -1f = 0 + -27 Combine like terms: 0 + -27 = -27 -1f = -27 Divide each side by '-1'. f = 27 Simplifying f = 27Solution
f = {16, 27}
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