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Simplifying 4b2(b + -6) = 108b Reorder the terms: 4b2(-6 + b) = 108b (-6 * 4b2 + b * 4b2) = 108b (-24b2 + 4b3) = 108b Solving -24b2 + 4b3 = 108b Solving for variable 'b'. Reorder the terms: -108b + -24b2 + 4b3 = 108b + -108b Combine like terms: 108b + -108b = 0 -108b + -24b2 + 4b3 = 0 Factor out the Greatest Common Factor (GCF), '4b'. 4b(-27 + -6b + b2) = 0 Factor a trinomial. 4b((-3 + -1b)(9 + -1b)) = 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 '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 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, -3, 9}
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