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Simplifying (4b + 1)(4b + 2) = 0 Reorder the terms: (1 + 4b)(4b + 2) = 0 Reorder the terms: (1 + 4b)(2 + 4b) = 0 Multiply (1 + 4b) * (2 + 4b) (1(2 + 4b) + 4b * (2 + 4b)) = 0 ((2 * 1 + 4b * 1) + 4b * (2 + 4b)) = 0 ((2 + 4b) + 4b * (2 + 4b)) = 0 (2 + 4b + (2 * 4b + 4b * 4b)) = 0 (2 + 4b + (8b + 16b2)) = 0 Combine like terms: 4b + 8b = 12b (2 + 12b + 16b2) = 0 Solving 2 + 12b + 16b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 6b + 8b2) = 0 Factor a trinomial. 2((1 + 2b)(1 + 4b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 2b)' equal to zero and attempt to solve: Simplifying 1 + 2b = 0 Solving 1 + 2b = 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 + 2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2b = 0 + -1 2b = 0 + -1 Combine like terms: 0 + -1 = -1 2b = -1 Divide each side by '2'. b = -0.5 Simplifying b = -0.5Subproblem 2
Set the factor '(1 + 4b)' equal to zero and attempt to solve: Simplifying 1 + 4b = 0 Solving 1 + 4b = 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 + 4b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4b = 0 + -1 4b = 0 + -1 Combine like terms: 0 + -1 = -1 4b = -1 Divide each side by '4'. b = -0.25 Simplifying b = -0.25Solution
b = {-0.5, -0.25}
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