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Simplifying 3b2(b + -5) = 108b Reorder the terms: 3b2(-5 + b) = 108b (-5 * 3b2 + b * 3b2) = 108b (-15b2 + 3b3) = 108b Solving -15b2 + 3b3 = 108b Solving for variable 'b'. Reorder the terms: -108b + -15b2 + 3b3 = 108b + -108b Combine like terms: 108b + -108b = 0 -108b + -15b2 + 3b3 = 0 Factor out the Greatest Common Factor (GCF), '3b'. 3b(-36 + -5b + b2) = 0 Factor a trinomial. 3b((-4 + -1b)(9 + -1b)) = 0 Ignore the factor 3.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 '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9Solution
b = {0, -4, 9}
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