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Simplifying 5b3 = 40b2 + -80b Reorder the terms: 5b3 = -80b + 40b2 Solving 5b3 = -80b + 40b2 Solving for variable 'b'. Reorder the terms: 80b + -40b2 + 5b3 = -80b + 40b2 + 80b + -40b2 Reorder the terms: 80b + -40b2 + 5b3 = -80b + 80b + 40b2 + -40b2 Combine like terms: -80b + 80b = 0 80b + -40b2 + 5b3 = 0 + 40b2 + -40b2 80b + -40b2 + 5b3 = 40b2 + -40b2 Combine like terms: 40b2 + -40b2 = 0 80b + -40b2 + 5b3 = 0 Factor out the Greatest Common Factor (GCF), '5b'. 5b(16 + -8b + b2) = 0 Factor a trinomial. 5b((4 + -1b)(4 + -1b)) = 0 Ignore the factor 5.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 '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 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 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Subproblem 3
Set the factor '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 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 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {0, 4, 4}
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