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Simplifying 5f4 + -20f3 + -60f2 = 0 Reorder the terms: -60f2 + -20f3 + 5f4 = 0 Solving -60f2 + -20f3 + 5f4 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '5f2'. 5f2(-12 + -4f + f2) = 0 Factor a trinomial. 5f2((-2 + -1f)(6 + -1f)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'f2' equal to zero and attempt to solve: Simplifying f2 = 0 Solving f2 = 0 Move all terms containing f to the left, all other terms to the right. Simplifying f2 = 0 Take the square root of each side: f = {0}Subproblem 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 = -2Subproblem 3
Set the factor '(6 + -1f)' equal to zero and attempt to solve: Simplifying 6 + -1f = 0 Solving 6 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1f = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1f = 0 + -6 -1f = 0 + -6 Combine like terms: 0 + -6 = -6 -1f = -6 Divide each side by '-1'. f = 6 Simplifying f = 6Solution
f = {0, -2, 6}
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