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Simplifying (3f + -3)(3f + -3) = 0 Reorder the terms: (-3 + 3f)(3f + -3) = 0 Reorder the terms: (-3 + 3f)(-3 + 3f) = 0 Multiply (-3 + 3f) * (-3 + 3f) (-3(-3 + 3f) + 3f * (-3 + 3f)) = 0 ((-3 * -3 + 3f * -3) + 3f * (-3 + 3f)) = 0 ((9 + -9f) + 3f * (-3 + 3f)) = 0 (9 + -9f + (-3 * 3f + 3f * 3f)) = 0 (9 + -9f + (-9f + 9f2)) = 0 Combine like terms: -9f + -9f = -18f (9 + -18f + 9f2) = 0 Solving 9 + -18f + 9f2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + -2f + f2) = 0 Factor a trinomial. 9((1 + -1f)(1 + -1f)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -1f)' equal to zero and attempt to solve: Simplifying 1 + -1f = 0 Solving 1 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1f = 0 + -1 -1f = 0 + -1 Combine like terms: 0 + -1 = -1 -1f = -1 Divide each side by '-1'. f = 1 Simplifying f = 1Subproblem 2
Set the factor '(1 + -1f)' equal to zero and attempt to solve: Simplifying 1 + -1f = 0 Solving 1 + -1f = 0 Move all terms containing f to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1f = 0 + -1 -1f = 0 + -1 Combine like terms: 0 + -1 = -1 -1f = -1 Divide each side by '-1'. f = 1 Simplifying f = 1Solution
f = {1, 1}
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