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Simplifying (f + -8)(f + 9) = 0 Reorder the terms: (-8 + f)(f + 9) = 0 Reorder the terms: (-8 + f)(9 + f) = 0 Multiply (-8 + f) * (9 + f) (-8(9 + f) + f(9 + f)) = 0 ((9 * -8 + f * -8) + f(9 + f)) = 0 ((-72 + -8f) + f(9 + f)) = 0 (-72 + -8f + (9 * f + f * f)) = 0 (-72 + -8f + (9f + f2)) = 0 Combine like terms: -8f + 9f = 1f (-72 + 1f + f2) = 0 Solving -72 + 1f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (-9 + -1f)(8 + -1f) = 0Subproblem 1
Set the factor '(-9 + -1f)' equal to zero and attempt to solve: Simplifying -9 + -1f = 0 Solving -9 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1f = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1f = 0 + 9 -1f = 0 + 9 Combine like terms: 0 + 9 = 9 -1f = 9 Divide each side by '-1'. f = -9 Simplifying f = -9Subproblem 2
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 = 8Solution
f = {-9, 8}
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