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Simplifying (3b + 4)(2b + 7) = 0 Reorder the terms: (4 + 3b)(2b + 7) = 0 Reorder the terms: (4 + 3b)(7 + 2b) = 0 Multiply (4 + 3b) * (7 + 2b) (4(7 + 2b) + 3b * (7 + 2b)) = 0 ((7 * 4 + 2b * 4) + 3b * (7 + 2b)) = 0 ((28 + 8b) + 3b * (7 + 2b)) = 0 (28 + 8b + (7 * 3b + 2b * 3b)) = 0 (28 + 8b + (21b + 6b2)) = 0 Combine like terms: 8b + 21b = 29b (28 + 29b + 6b2) = 0 Solving 28 + 29b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + 2b)(4 + 3b) = 0Subproblem 1
Set the factor '(7 + 2b)' equal to zero and attempt to solve: Simplifying 7 + 2b = 0 Solving 7 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2b = 0 + -7 2b = 0 + -7 Combine like terms: 0 + -7 = -7 2b = -7 Divide each side by '2'. b = -3.5 Simplifying b = -3.5Subproblem 2
Set the factor '(4 + 3b)' equal to zero and attempt to solve: Simplifying 4 + 3b = 0 Solving 4 + 3b = 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 + 3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3b = 0 + -4 3b = 0 + -4 Combine like terms: 0 + -4 = -4 3b = -4 Divide each side by '3'. b = -1.333333333 Simplifying b = -1.333333333Solution
b = {-3.5, -1.333333333}
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