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Simplifying (4b + 9)(b + 8) = 0 Reorder the terms: (9 + 4b)(b + 8) = 0 Reorder the terms: (9 + 4b)(8 + b) = 0 Multiply (9 + 4b) * (8 + b) (9(8 + b) + 4b * (8 + b)) = 0 ((8 * 9 + b * 9) + 4b * (8 + b)) = 0 ((72 + 9b) + 4b * (8 + b)) = 0 (72 + 9b + (8 * 4b + b * 4b)) = 0 (72 + 9b + (32b + 4b2)) = 0 Combine like terms: 9b + 32b = 41b (72 + 41b + 4b2) = 0 Solving 72 + 41b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (8 + b)(9 + 4b) = 0Subproblem 1
Set the factor '(8 + b)' equal to zero and attempt to solve: Simplifying 8 + b = 0 Solving 8 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + b = 0 + -8 b = 0 + -8 Combine like terms: 0 + -8 = -8 b = -8 Simplifying b = -8Subproblem 2
Set the factor '(9 + 4b)' equal to zero and attempt to solve: Simplifying 9 + 4b = 0 Solving 9 + 4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4b = 0 + -9 4b = 0 + -9 Combine like terms: 0 + -9 = -9 4b = -9 Divide each side by '4'. b = -2.25 Simplifying b = -2.25Solution
b = {-8, -2.25}
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