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Simplifying (15 + 3b)(15 + 5b) = 0 Multiply (15 + 3b) * (15 + 5b) (15(15 + 5b) + 3b * (15 + 5b)) = 0 ((15 * 15 + 5b * 15) + 3b * (15 + 5b)) = 0 ((225 + 75b) + 3b * (15 + 5b)) = 0 (225 + 75b + (15 * 3b + 5b * 3b)) = 0 (225 + 75b + (45b + 15b2)) = 0 Combine like terms: 75b + 45b = 120b (225 + 120b + 15b2) = 0 Solving 225 + 120b + 15b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '15'. 15(15 + 8b + b2) = 0 Factor a trinomial. 15((5 + b)(3 + b)) = 0 Ignore the factor 15.Subproblem 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 '(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 = -3Solution
b = {-5, -3}
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