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Simplifying 48r2 + 72rf + 27f2 = 0 Reorder the terms: 72fr + 27f2 + 48r2 = 0 Solving 72fr + 27f2 + 48r2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(24fr + 9f2 + 16r2) = 0 Factor a trinomial. 3((3f + 4r)(3f + 4r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3f + 4r)' equal to zero and attempt to solve: Simplifying 3f + 4r = 0 Solving 3f + 4r = 0 Move all terms containing f to the left, all other terms to the right. Add '-4r' to each side of the equation. 3f + 4r + -4r = 0 + -4r Combine like terms: 4r + -4r = 0 3f + 0 = 0 + -4r 3f = 0 + -4r Remove the zero: 3f = -4r Divide each side by '3'. f = -1.333333333r Simplifying f = -1.333333333rSubproblem 2
Set the factor '(3f + 4r)' equal to zero and attempt to solve: Simplifying 3f + 4r = 0 Solving 3f + 4r = 0 Move all terms containing f to the left, all other terms to the right. Add '-4r' to each side of the equation. 3f + 4r + -4r = 0 + -4r Combine like terms: 4r + -4r = 0 3f + 0 = 0 + -4r 3f = 0 + -4r Remove the zero: 3f = -4r Divide each side by '3'. f = -1.333333333r Simplifying f = -1.333333333rSolution
f = {-1.333333333r, -1.333333333r}
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