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Simplifying (4b + 3)(b + 1) = 0 Reorder the terms: (3 + 4b)(b + 1) = 0 Reorder the terms: (3 + 4b)(1 + b) = 0 Multiply (3 + 4b) * (1 + b) (3(1 + b) + 4b * (1 + b)) = 0 ((1 * 3 + b * 3) + 4b * (1 + b)) = 0 ((3 + 3b) + 4b * (1 + b)) = 0 (3 + 3b + (1 * 4b + b * 4b)) = 0 (3 + 3b + (4b + 4b2)) = 0 Combine like terms: 3b + 4b = 7b (3 + 7b + 4b2) = 0 Solving 3 + 7b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (1 + b)(3 + 4b) = 0Subproblem 1
Set the factor '(1 + b)' equal to zero and attempt to solve: Simplifying 1 + b = 0 Solving 1 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + b = 0 + -1 b = 0 + -1 Combine like terms: 0 + -1 = -1 b = -1 Simplifying b = -1Subproblem 2
Set the factor '(3 + 4b)' equal to zero and attempt to solve: Simplifying 3 + 4b = 0 Solving 3 + 4b = 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 + 4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4b = 0 + -3 4b = 0 + -3 Combine like terms: 0 + -3 = -3 4b = -3 Divide each side by '4'. b = -0.75 Simplifying b = -0.75Solution
b = {-1, -0.75}
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