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Simplifying 7(b + 1)(b + 1) + 13(b + 1) + -2 = 0 Reorder the terms: 7(1 + b)(b + 1) + 13(b + 1) + -2 = 0 Reorder the terms: 7(1 + b)(1 + b) + 13(b + 1) + -2 = 0 Multiply (1 + b) * (1 + b) 7(1(1 + b) + b(1 + b)) + 13(b + 1) + -2 = 0 7((1 * 1 + b * 1) + b(1 + b)) + 13(b + 1) + -2 = 0 7((1 + 1b) + b(1 + b)) + 13(b + 1) + -2 = 0 7(1 + 1b + (1 * b + b * b)) + 13(b + 1) + -2 = 0 7(1 + 1b + (1b + b2)) + 13(b + 1) + -2 = 0 Combine like terms: 1b + 1b = 2b 7(1 + 2b + b2) + 13(b + 1) + -2 = 0 (1 * 7 + 2b * 7 + b2 * 7) + 13(b + 1) + -2 = 0 (7 + 14b + 7b2) + 13(b + 1) + -2 = 0 Reorder the terms: 7 + 14b + 7b2 + 13(1 + b) + -2 = 0 7 + 14b + 7b2 + (1 * 13 + b * 13) + -2 = 0 7 + 14b + 7b2 + (13 + 13b) + -2 = 0 Reorder the terms: 7 + 13 + -2 + 14b + 13b + 7b2 = 0 Combine like terms: 7 + 13 = 20 20 + -2 + 14b + 13b + 7b2 = 0 Combine like terms: 20 + -2 = 18 18 + 14b + 13b + 7b2 = 0 Combine like terms: 14b + 13b = 27b 18 + 27b + 7b2 = 0 Solving 18 + 27b + 7b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + b)(6 + 7b) = 0Subproblem 1
Set the factor '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Subproblem 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 = {-3, -0.8571428571}
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