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Simplifying 2b(b + 3) + 5(b + 3) = 0 Reorder the terms: 2b(3 + b) + 5(b + 3) = 0 (3 * 2b + b * 2b) + 5(b + 3) = 0 (6b + 2b2) + 5(b + 3) = 0 Reorder the terms: 6b + 2b2 + 5(3 + b) = 0 6b + 2b2 + (3 * 5 + b * 5) = 0 6b + 2b2 + (15 + 5b) = 0 Reorder the terms: 15 + 6b + 5b + 2b2 = 0 Combine like terms: 6b + 5b = 11b 15 + 11b + 2b2 = 0 Solving 15 + 11b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + b)(5 + 2b) = 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 '(5 + 2b)' equal to zero and attempt to solve: Simplifying 5 + 2b = 0 Solving 5 + 2b = 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 + 2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2b = 0 + -5 2b = 0 + -5 Combine like terms: 0 + -5 = -5 2b = -5 Divide each side by '2'. b = -2.5 Simplifying b = -2.5Solution
b = {-3, -2.5}
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