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Simplifying (8b + 9)(7b + 6) = 0 Reorder the terms: (9 + 8b)(7b + 6) = 0 Reorder the terms: (9 + 8b)(6 + 7b) = 0 Multiply (9 + 8b) * (6 + 7b) (9(6 + 7b) + 8b * (6 + 7b)) = 0 ((6 * 9 + 7b * 9) + 8b * (6 + 7b)) = 0 ((54 + 63b) + 8b * (6 + 7b)) = 0 (54 + 63b + (6 * 8b + 7b * 8b)) = 0 (54 + 63b + (48b + 56b2)) = 0 Combine like terms: 63b + 48b = 111b (54 + 111b + 56b2) = 0 Solving 54 + 111b + 56b2 = 0 Solving for variable 'b'. Factor a trinomial. (9 + 8b)(6 + 7b) = 0Subproblem 1
Set the factor '(9 + 8b)' equal to zero and attempt to solve: Simplifying 9 + 8b = 0 Solving 9 + 8b = 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 + 8b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8b = 0 + -9 8b = 0 + -9 Combine like terms: 0 + -9 = -9 8b = -9 Divide each side by '8'. b = -1.125 Simplifying b = -1.125Subproblem 2
Set the factor '(6 + 7b)' equal to zero and attempt to solve: Simplifying 6 + 7b = 0 Solving 6 + 7b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7b = 0 + -6 7b = 0 + -6 Combine like terms: 0 + -6 = -6 7b = -6 Divide each side by '7'. b = -0.8571428571 Simplifying b = -0.8571428571Solution
b = {-1.125, -0.8571428571}
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