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Simplifying (4b + 7)(4b + 8) = 0 Reorder the terms: (7 + 4b)(4b + 8) = 0 Reorder the terms: (7 + 4b)(8 + 4b) = 0 Multiply (7 + 4b) * (8 + 4b) (7(8 + 4b) + 4b * (8 + 4b)) = 0 ((8 * 7 + 4b * 7) + 4b * (8 + 4b)) = 0 ((56 + 28b) + 4b * (8 + 4b)) = 0 (56 + 28b + (8 * 4b + 4b * 4b)) = 0 (56 + 28b + (32b + 16b2)) = 0 Combine like terms: 28b + 32b = 60b (56 + 60b + 16b2) = 0 Solving 56 + 60b + 16b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(14 + 15b + 4b2) = 0 Factor a trinomial. 4((2 + b)(7 + 4b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + b)' equal to zero and attempt to solve: Simplifying 2 + b = 0 Solving 2 + b = 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 + b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + b = 0 + -2 b = 0 + -2 Combine like terms: 0 + -2 = -2 b = -2 Simplifying b = -2Subproblem 2
Set the factor '(7 + 4b)' equal to zero and attempt to solve: Simplifying 7 + 4b = 0 Solving 7 + 4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4b = 0 + -7 4b = 0 + -7 Combine like terms: 0 + -7 = -7 4b = -7 Divide each side by '4'. b = -1.75 Simplifying b = -1.75Solution
b = {-2, -1.75}
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