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Simplifying 5b(7b + -5)(5b + -1) = 0 Reorder the terms: 5b(-5 + 7b)(5b + -1) = 0 Reorder the terms: 5b(-5 + 7b)(-1 + 5b) = 0 Multiply (-5 + 7b) * (-1 + 5b) 5b(-5(-1 + 5b) + 7b * (-1 + 5b)) = 0 5b((-1 * -5 + 5b * -5) + 7b * (-1 + 5b)) = 0 5b((5 + -25b) + 7b * (-1 + 5b)) = 0 5b(5 + -25b + (-1 * 7b + 5b * 7b)) = 0 5b(5 + -25b + (-7b + 35b2)) = 0 Combine like terms: -25b + -7b = -32b 5b(5 + -32b + 35b2) = 0 (5 * 5b + -32b * 5b + 35b2 * 5b) = 0 (25b + -160b2 + 175b3) = 0 Solving 25b + -160b2 + 175b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5b'. 5b(5 + -32b + 35b2) = 0 Factor a trinomial. 5b((1 + -5b)(5 + -7b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(1 + -5b)' equal to zero and attempt to solve: Simplifying 1 + -5b = 0 Solving 1 + -5b = 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 + -5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5b = 0 + -1 -5b = 0 + -1 Combine like terms: 0 + -1 = -1 -5b = -1 Divide each side by '-5'. b = 0.2 Simplifying b = 0.2Subproblem 3
Set the factor '(5 + -7b)' equal to zero and attempt to solve: Simplifying 5 + -7b = 0 Solving 5 + -7b = 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 + -7b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7b = 0 + -5 -7b = 0 + -5 Combine like terms: 0 + -5 = -5 -7b = -5 Divide each side by '-7'. b = 0.7142857143 Simplifying b = 0.7142857143Solution
b = {0, 0.2, 0.7142857143}
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