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Simplifying (2b + 7)(b + 3) = 0 Reorder the terms: (7 + 2b)(b + 3) = 0 Reorder the terms: (7 + 2b)(3 + b) = 0 Multiply (7 + 2b) * (3 + b) (7(3 + b) + 2b * (3 + b)) = 0 ((3 * 7 + b * 7) + 2b * (3 + b)) = 0 ((21 + 7b) + 2b * (3 + b)) = 0 (21 + 7b + (3 * 2b + b * 2b)) = 0 (21 + 7b + (6b + 2b2)) = 0 Combine like terms: 7b + 6b = 13b (21 + 13b + 2b2) = 0 Solving 21 + 13b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + 2b)(3 + b) = 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 '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 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 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Solution
b = {-3.5, -3}
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