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Simplifying 24b3 + 92b2 + 80b = 0 Reorder the terms: 80b + 92b2 + 24b3 = 0 Solving 80b + 92b2 + 24b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4b'. 4b(20 + 23b + 6b2) = 0 Factor a trinomial. 4b((5 + 2b)(4 + 3b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(5 + 2b)' equal to zero and attempt to solve: Simplifying 5 + 2b = 0 Solving 5 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2b = 0 + -5 2b = 0 + -5 Combine like terms: 0 + -5 = -5 2b = -5 Divide each side by '2'. b = -2.5 Simplifying b = -2.5Subproblem 3
Set the factor '(4 + 3b)' equal to zero and attempt to solve: Simplifying 4 + 3b = 0 Solving 4 + 3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3b = 0 + -4 3b = 0 + -4 Combine like terms: 0 + -4 = -4 3b = -4 Divide each side by '3'. b = -1.333333333 Simplifying b = -1.333333333Solution
b = {0, -2.5, -1.333333333}
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