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Simplifying (3b + 5)(b + 5) = 0 Reorder the terms: (5 + 3b)(b + 5) = 0 Reorder the terms: (5 + 3b)(5 + b) = 0 Multiply (5 + 3b) * (5 + b) (5(5 + b) + 3b * (5 + b)) = 0 ((5 * 5 + b * 5) + 3b * (5 + b)) = 0 ((25 + 5b) + 3b * (5 + b)) = 0 (25 + 5b + (5 * 3b + b * 3b)) = 0 (25 + 5b + (15b + 3b2)) = 0 Combine like terms: 5b + 15b = 20b (25 + 20b + 3b2) = 0 Solving 25 + 20b + 3b2 = 0 Solving for variable 'b'. Factor a trinomial. (5 + b)(5 + 3b) = 0Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve: Simplifying 5 + b = 0 Solving 5 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + b = 0 + -5 b = 0 + -5 Combine like terms: 0 + -5 = -5 b = -5 Simplifying b = -5Subproblem 2
Set the factor '(5 + 3b)' equal to zero and attempt to solve: Simplifying 5 + 3b = 0 Solving 5 + 3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3b = 0 + -5 3b = 0 + -5 Combine like terms: 0 + -5 = -5 3b = -5 Divide each side by '3'. b = -1.666666667 Simplifying b = -1.666666667Solution
b = {-5, -1.666666667}
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