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Simplifying (3b + 5)(b + 3) + -7 = 0 Reorder the terms: (5 + 3b)(b + 3) + -7 = 0 Reorder the terms: (5 + 3b)(3 + b) + -7 = 0 Multiply (5 + 3b) * (3 + b) (5(3 + b) + 3b * (3 + b)) + -7 = 0 ((3 * 5 + b * 5) + 3b * (3 + b)) + -7 = 0 ((15 + 5b) + 3b * (3 + b)) + -7 = 0 (15 + 5b + (3 * 3b + b * 3b)) + -7 = 0 (15 + 5b + (9b + 3b2)) + -7 = 0 Combine like terms: 5b + 9b = 14b (15 + 14b + 3b2) + -7 = 0 Reorder the terms: 15 + -7 + 14b + 3b2 = 0 Combine like terms: 15 + -7 = 8 8 + 14b + 3b2 = 0 Solving 8 + 14b + 3b2 = 0 Solving for variable 'b'. Factor a trinomial. (4 + b)(2 + 3b) = 0Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve: Simplifying 4 + b = 0 Solving 4 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + b = 0 + -4 b = 0 + -4 Combine like terms: 0 + -4 = -4 b = -4 Simplifying b = -4Subproblem 2
Set the factor '(2 + 3b)' equal to zero and attempt to solve: Simplifying 2 + 3b = 0 Solving 2 + 3b = 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 + 3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3b = 0 + -2 3b = 0 + -2 Combine like terms: 0 + -2 = -2 3b = -2 Divide each side by '3'. b = -0.6666666667 Simplifying b = -0.6666666667Solution
b = {-4, -0.6666666667}
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