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Simplifying (11b + 6)(12b + 8) + (7b + 5)(11b + 6) = 0 Reorder the terms: (6 + 11b)(12b + 8) + (7b + 5)(11b + 6) = 0 Reorder the terms: (6 + 11b)(8 + 12b) + (7b + 5)(11b + 6) = 0 Multiply (6 + 11b) * (8 + 12b) (6(8 + 12b) + 11b * (8 + 12b)) + (7b + 5)(11b + 6) = 0 ((8 * 6 + 12b * 6) + 11b * (8 + 12b)) + (7b + 5)(11b + 6) = 0 ((48 + 72b) + 11b * (8 + 12b)) + (7b + 5)(11b + 6) = 0 (48 + 72b + (8 * 11b + 12b * 11b)) + (7b + 5)(11b + 6) = 0 (48 + 72b + (88b + 132b2)) + (7b + 5)(11b + 6) = 0 Combine like terms: 72b + 88b = 160b (48 + 160b + 132b2) + (7b + 5)(11b + 6) = 0 Reorder the terms: 48 + 160b + 132b2 + (5 + 7b)(11b + 6) = 0 Reorder the terms: 48 + 160b + 132b2 + (5 + 7b)(6 + 11b) = 0 Multiply (5 + 7b) * (6 + 11b) 48 + 160b + 132b2 + (5(6 + 11b) + 7b * (6 + 11b)) = 0 48 + 160b + 132b2 + ((6 * 5 + 11b * 5) + 7b * (6 + 11b)) = 0 48 + 160b + 132b2 + ((30 + 55b) + 7b * (6 + 11b)) = 0 48 + 160b + 132b2 + (30 + 55b + (6 * 7b + 11b * 7b)) = 0 48 + 160b + 132b2 + (30 + 55b + (42b + 77b2)) = 0 Combine like terms: 55b + 42b = 97b 48 + 160b + 132b2 + (30 + 97b + 77b2) = 0 Reorder the terms: 48 + 30 + 160b + 97b + 132b2 + 77b2 = 0 Combine like terms: 48 + 30 = 78 78 + 160b + 97b + 132b2 + 77b2 = 0 Combine like terms: 160b + 97b = 257b 78 + 257b + 132b2 + 77b2 = 0 Combine like terms: 132b2 + 77b2 = 209b2 78 + 257b + 209b2 = 0 Solving 78 + 257b + 209b2 = 0 Solving for variable 'b'. Factor a trinomial. (13 + 19b)(6 + 11b) = 0Subproblem 1
Set the factor '(13 + 19b)' equal to zero and attempt to solve: Simplifying 13 + 19b = 0 Solving 13 + 19b = 0 Move all terms containing b to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 19b = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 19b = 0 + -13 19b = 0 + -13 Combine like terms: 0 + -13 = -13 19b = -13 Divide each side by '19'. b = -0.6842105263 Simplifying b = -0.6842105263Subproblem 2
Set the factor '(6 + 11b)' equal to zero and attempt to solve: Simplifying 6 + 11b = 0 Solving 6 + 11b = 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 + 11b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 11b = 0 + -6 11b = 0 + -6 Combine like terms: 0 + -6 = -6 11b = -6 Divide each side by '11'. b = -0.5454545455 Simplifying b = -0.5454545455Solution
b = {-0.6842105263, -0.5454545455}
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