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Simplifying (f + -10)(f + -12) = 0 Reorder the terms: (-10 + f)(f + -12) = 0 Reorder the terms: (-10 + f)(-12 + f) = 0 Multiply (-10 + f) * (-12 + f) (-10(-12 + f) + f(-12 + f)) = 0 ((-12 * -10 + f * -10) + f(-12 + f)) = 0 ((120 + -10f) + f(-12 + f)) = 0 (120 + -10f + (-12 * f + f * f)) = 0 (120 + -10f + (-12f + f2)) = 0 Combine like terms: -10f + -12f = -22f (120 + -22f + f2) = 0 Solving 120 + -22f + f2 = 0 Solving for variable 'f'. Factor a trinomial. (10 + -1f)(12 + -1f) = 0Subproblem 1
Set the factor '(10 + -1f)' equal to zero and attempt to solve: Simplifying 10 + -1f = 0 Solving 10 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1f = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1f = 0 + -10 -1f = 0 + -10 Combine like terms: 0 + -10 = -10 -1f = -10 Divide each side by '-1'. f = 10 Simplifying f = 10Subproblem 2
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 = 12Solution
f = {10, 12}
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