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Simplifying 24w4 + 54w3b + -15w2b2 = 0 Reorder the terms: 54bw3 + -15b2w2 + 24w4 = 0 Solving 54bw3 + -15b2w2 + 24w4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3w2'. 3w2(18bw + -5b2 + 8w2) = 0 Factor a trinomial. 3w2((-5b + -2w)(b + -4w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1w2' to each side of the equation. w2 + -1w2 = 0 + -1w2 Remove the zero: 0 = -1w2 Simplifying 0 = -1w2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5b + -2w)' equal to zero and attempt to solve: Simplifying -5b + -2w = 0 Solving -5b + -2w = 0 Move all terms containing b to the left, all other terms to the right. Add '2w' to each side of the equation. -5b + -2w + 2w = 0 + 2w Combine like terms: -2w + 2w = 0 -5b + 0 = 0 + 2w -5b = 0 + 2w Remove the zero: -5b = 2w Divide each side by '-5'. b = -0.4w Simplifying b = -0.4wSubproblem 3
Set the factor '(b + -4w)' equal to zero and attempt to solve: Simplifying b + -4w = 0 Solving b + -4w = 0 Move all terms containing b to the left, all other terms to the right. Add '4w' to each side of the equation. b + -4w + 4w = 0 + 4w Combine like terms: -4w + 4w = 0 b + 0 = 0 + 4w b = 0 + 4w Remove the zero: b = 4w Simplifying b = 4wSolution
b = {-0.4w, 4w}
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