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Simplifying 12v2 + 36vf + 27f2 = 0 Reorder the terms: 36fv + 27f2 + 12v2 = 0 Solving 36fv + 27f2 + 12v2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(12fv + 9f2 + 4v2) = 0 Factor a trinomial. 3((3f + 2v)(3f + 2v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3f + 2v)' equal to zero and attempt to solve: Simplifying 3f + 2v = 0 Solving 3f + 2v = 0 Move all terms containing f to the left, all other terms to the right. Add '-2v' to each side of the equation. 3f + 2v + -2v = 0 + -2v Combine like terms: 2v + -2v = 0 3f + 0 = 0 + -2v 3f = 0 + -2v Remove the zero: 3f = -2v Divide each side by '3'. f = -0.6666666667v Simplifying f = -0.6666666667vSubproblem 2
Set the factor '(3f + 2v)' equal to zero and attempt to solve: Simplifying 3f + 2v = 0 Solving 3f + 2v = 0 Move all terms containing f to the left, all other terms to the right. Add '-2v' to each side of the equation. 3f + 2v + -2v = 0 + -2v Combine like terms: 2v + -2v = 0 3f + 0 = 0 + -2v 3f = 0 + -2v Remove the zero: 3f = -2v Divide each side by '3'. f = -0.6666666667v Simplifying f = -0.6666666667vSolution
f = {-0.6666666667v, -0.6666666667v}
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