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Simplifying 2b(7b + -2)(2b + -1) = 0 Reorder the terms: 2b(-2 + 7b)(2b + -1) = 0 Reorder the terms: 2b(-2 + 7b)(-1 + 2b) = 0 Multiply (-2 + 7b) * (-1 + 2b) 2b(-2(-1 + 2b) + 7b * (-1 + 2b)) = 0 2b((-1 * -2 + 2b * -2) + 7b * (-1 + 2b)) = 0 2b((2 + -4b) + 7b * (-1 + 2b)) = 0 2b(2 + -4b + (-1 * 7b + 2b * 7b)) = 0 2b(2 + -4b + (-7b + 14b2)) = 0 Combine like terms: -4b + -7b = -11b 2b(2 + -11b + 14b2) = 0 (2 * 2b + -11b * 2b + 14b2 * 2b) = 0 (4b + -22b2 + 28b3) = 0 Solving 4b + -22b2 + 28b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2b'. 2b(2 + -11b + 14b2) = 0 Factor a trinomial. 2b((2 + -7b)(1 + -2b)) = 0 Ignore the factor 2.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 '(2 + -7b)' equal to zero and attempt to solve: Simplifying 2 + -7b = 0 Solving 2 + -7b = 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 + -7b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7b = 0 + -2 -7b = 0 + -2 Combine like terms: 0 + -2 = -2 -7b = -2 Divide each side by '-7'. b = 0.2857142857 Simplifying b = 0.2857142857Subproblem 3
Set the factor '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 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 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Solution
b = {0, 0.2857142857, 0.5}
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