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Simplifying 12w2 + 36wf + 27f2 = 0 Reorder the terms: 36fw + 27f2 + 12w2 = 0 Solving 36fw + 27f2 + 12w2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(12fw + 9f2 + 4w2) = 0 Factor a trinomial. 3((3f + 2w)(3f + 2w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3f + 2w)' equal to zero and attempt to solve: Simplifying 3f + 2w = 0 Solving 3f + 2w = 0 Move all terms containing f to the left, all other terms to the right. Add '-2w' to each side of the equation. 3f + 2w + -2w = 0 + -2w Combine like terms: 2w + -2w = 0 3f + 0 = 0 + -2w 3f = 0 + -2w Remove the zero: 3f = -2w Divide each side by '3'. f = -0.6666666667w Simplifying f = -0.6666666667wSubproblem 2
Set the factor '(3f + 2w)' equal to zero and attempt to solve: Simplifying 3f + 2w = 0 Solving 3f + 2w = 0 Move all terms containing f to the left, all other terms to the right. Add '-2w' to each side of the equation. 3f + 2w + -2w = 0 + -2w Combine like terms: 2w + -2w = 0 3f + 0 = 0 + -2w 3f = 0 + -2w Remove the zero: 3f = -2w Divide each side by '3'. f = -0.6666666667w Simplifying f = -0.6666666667wSolution
f = {-0.6666666667w, -0.6666666667w}
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