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Simplifying (2b + 2)(3b + 1) = 0 Reorder the terms: (2 + 2b)(3b + 1) = 0 Reorder the terms: (2 + 2b)(1 + 3b) = 0 Multiply (2 + 2b) * (1 + 3b) (2(1 + 3b) + 2b * (1 + 3b)) = 0 ((1 * 2 + 3b * 2) + 2b * (1 + 3b)) = 0 ((2 + 6b) + 2b * (1 + 3b)) = 0 (2 + 6b + (1 * 2b + 3b * 2b)) = 0 (2 + 6b + (2b + 6b2)) = 0 Combine like terms: 6b + 2b = 8b (2 + 8b + 6b2) = 0 Solving 2 + 8b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 4b + 3b2) = 0 Factor a trinomial. 2((1 + b)(1 + 3b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + b)' equal to zero and attempt to solve: Simplifying 1 + b = 0 Solving 1 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + b = 0 + -1 b = 0 + -1 Combine like terms: 0 + -1 = -1 b = -1 Simplifying b = -1Subproblem 2
Set the factor '(1 + 3b)' equal to zero and attempt to solve: Simplifying 1 + 3b = 0 Solving 1 + 3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3b = 0 + -1 3b = 0 + -1 Combine like terms: 0 + -1 = -1 3b = -1 Divide each side by '3'. b = -0.3333333333 Simplifying b = -0.3333333333Solution
b = {-1, -0.3333333333}
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