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Simplifying (7b + 14)(6b + 9) + -1(8b + 10)(7b + 14) = 0 Reorder the terms: (14 + 7b)(6b + 9) + -1(8b + 10)(7b + 14) = 0 Reorder the terms: (14 + 7b)(9 + 6b) + -1(8b + 10)(7b + 14) = 0 Multiply (14 + 7b) * (9 + 6b) (14(9 + 6b) + 7b * (9 + 6b)) + -1(8b + 10)(7b + 14) = 0 ((9 * 14 + 6b * 14) + 7b * (9 + 6b)) + -1(8b + 10)(7b + 14) = 0 ((126 + 84b) + 7b * (9 + 6b)) + -1(8b + 10)(7b + 14) = 0 (126 + 84b + (9 * 7b + 6b * 7b)) + -1(8b + 10)(7b + 14) = 0 (126 + 84b + (63b + 42b2)) + -1(8b + 10)(7b + 14) = 0 Combine like terms: 84b + 63b = 147b (126 + 147b + 42b2) + -1(8b + 10)(7b + 14) = 0 Reorder the terms: 126 + 147b + 42b2 + -1(10 + 8b)(7b + 14) = 0 Reorder the terms: 126 + 147b + 42b2 + -1(10 + 8b)(14 + 7b) = 0 Multiply (10 + 8b) * (14 + 7b) 126 + 147b + 42b2 + -1(10(14 + 7b) + 8b * (14 + 7b)) = 0 126 + 147b + 42b2 + -1((14 * 10 + 7b * 10) + 8b * (14 + 7b)) = 0 126 + 147b + 42b2 + -1((140 + 70b) + 8b * (14 + 7b)) = 0 126 + 147b + 42b2 + -1(140 + 70b + (14 * 8b + 7b * 8b)) = 0 126 + 147b + 42b2 + -1(140 + 70b + (112b + 56b2)) = 0 Combine like terms: 70b + 112b = 182b 126 + 147b + 42b2 + -1(140 + 182b + 56b2) = 0 126 + 147b + 42b2 + (140 * -1 + 182b * -1 + 56b2 * -1) = 0 126 + 147b + 42b2 + (-140 + -182b + -56b2) = 0 Reorder the terms: 126 + -140 + 147b + -182b + 42b2 + -56b2 = 0 Combine like terms: 126 + -140 = -14 -14 + 147b + -182b + 42b2 + -56b2 = 0 Combine like terms: 147b + -182b = -35b -14 + -35b + 42b2 + -56b2 = 0 Combine like terms: 42b2 + -56b2 = -14b2 -14 + -35b + -14b2 = 0 Solving -14 + -35b + -14b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-7'. -7(2 + 5b + 2b2) = 0 Factor a trinomial. -7((2 + b)(1 + 2b)) = 0 Ignore the factor -7.Subproblem 1
Set the factor '(2 + b)' equal to zero and attempt to solve: Simplifying 2 + b = 0 Solving 2 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + b = 0 + -2 b = 0 + -2 Combine like terms: 0 + -2 = -2 b = -2 Simplifying b = -2Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve: Simplifying 1 + 2b = 0 Solving 1 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2b = 0 + -1 2b = 0 + -1 Combine like terms: 0 + -1 = -1 2b = -1 Divide each side by '2'. b = -0.5 Simplifying b = -0.5Solution
b = {-2, -0.5}
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