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Simplifying (2b + 5)(b + 4) = 0 Reorder the terms: (5 + 2b)(b + 4) = 0 Reorder the terms: (5 + 2b)(4 + b) = 0 Multiply (5 + 2b) * (4 + b) (5(4 + b) + 2b * (4 + b)) = 0 ((4 * 5 + b * 5) + 2b * (4 + b)) = 0 ((20 + 5b) + 2b * (4 + b)) = 0 (20 + 5b + (4 * 2b + b * 2b)) = 0 (20 + 5b + (8b + 2b2)) = 0 Combine like terms: 5b + 8b = 13b (20 + 13b + 2b2) = 0 Solving 20 + 13b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (4 + b)(5 + 2b) = 0Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve: Simplifying 4 + b = 0 Solving 4 + b = 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 + b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + b = 0 + -4 b = 0 + -4 Combine like terms: 0 + -4 = -4 b = -4 Simplifying b = -4Subproblem 2
Set the factor '(5 + 2b)' equal to zero and attempt to solve: Simplifying 5 + 2b = 0 Solving 5 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2b = 0 + -5 2b = 0 + -5 Combine like terms: 0 + -5 = -5 2b = -5 Divide each side by '2'. b = -2.5 Simplifying b = -2.5Solution
b = {-4, -2.5}
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