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Simplifying 2b(2b + 6) + b(8b + 6) = 0 Reorder the terms: 2b(6 + 2b) + b(8b + 6) = 0 (6 * 2b + 2b * 2b) + b(8b + 6) = 0 (12b + 4b2) + b(8b + 6) = 0 Reorder the terms: 12b + 4b2 + b(6 + 8b) = 0 12b + 4b2 + (6 * b + 8b * b) = 0 12b + 4b2 + (6b + 8b2) = 0 Reorder the terms: 12b + 6b + 4b2 + 8b2 = 0 Combine like terms: 12b + 6b = 18b 18b + 4b2 + 8b2 = 0 Combine like terms: 4b2 + 8b2 = 12b2 18b + 12b2 = 0 Solving 18b + 12b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6b'. 6b(3 + 2b) = 0 Ignore the factor 6.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 + 2b)' equal to zero and attempt to solve: Simplifying 3 + 2b = 0 Solving 3 + 2b = 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 + 2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2b = 0 + -3 2b = 0 + -3 Combine like terms: 0 + -3 = -3 2b = -3 Divide each side by '2'. b = -1.5 Simplifying b = -1.5Solution
b = {0, -1.5}
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