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Simplifying (f + 12)(f + -15) = 0 Reorder the terms: (12 + f)(f + -15) = 0 Reorder the terms: (12 + f)(-15 + f) = 0 Multiply (12 + f) * (-15 + f) (12(-15 + f) + f(-15 + f)) = 0 ((-15 * 12 + f * 12) + f(-15 + f)) = 0 ((-180 + 12f) + f(-15 + f)) = 0 (-180 + 12f + (-15 * f + f * f)) = 0 (-180 + 12f + (-15f + f2)) = 0 Combine like terms: 12f + -15f = -3f (-180 + -3f + f2) = 0 Solving -180 + -3f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (-12 + -1f)(15 + -1f) = 0Subproblem 1
Set the factor '(-12 + -1f)' equal to zero and attempt to solve: Simplifying -12 + -1f = 0 Solving -12 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1f = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1f = 0 + 12 -1f = 0 + 12 Combine like terms: 0 + 12 = 12 -1f = 12 Divide each side by '-1'. f = -12 Simplifying f = -12Subproblem 2
Set the factor '(15 + -1f)' equal to zero and attempt to solve: Simplifying 15 + -1f = 0 Solving 15 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1f = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1f = 0 + -15 -1f = 0 + -15 Combine like terms: 0 + -15 = -15 -1f = -15 Divide each side by '-1'. f = 15 Simplifying f = 15Solution
f = {-12, 15}
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