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Simplifying 7(5b + 7)(b + 1) = 0 Reorder the terms: 7(7 + 5b)(b + 1) = 0 Reorder the terms: 7(7 + 5b)(1 + b) = 0 Multiply (7 + 5b) * (1 + b) 7(7(1 + b) + 5b * (1 + b)) = 0 7((1 * 7 + b * 7) + 5b * (1 + b)) = 0 7((7 + 7b) + 5b * (1 + b)) = 0 7(7 + 7b + (1 * 5b + b * 5b)) = 0 7(7 + 7b + (5b + 5b2)) = 0 Combine like terms: 7b + 5b = 12b 7(7 + 12b + 5b2) = 0 (7 * 7 + 12b * 7 + 5b2 * 7) = 0 (49 + 84b + 35b2) = 0 Solving 49 + 84b + 35b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '7'. 7(7 + 12b + 5b2) = 0 Factor a trinomial. 7((7 + 5b)(1 + b)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(7 + 5b)' equal to zero and attempt to solve: Simplifying 7 + 5b = 0 Solving 7 + 5b = 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 + 5b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5b = 0 + -7 5b = 0 + -7 Combine like terms: 0 + -7 = -7 5b = -7 Divide each side by '5'. b = -1.4 Simplifying b = -1.4Subproblem 2
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 = -1Solution
b = {-1.4, -1}
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