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Simplifying 4b(3b + -4)(4b + -1) = 0 Reorder the terms: 4b(-4 + 3b)(4b + -1) = 0 Reorder the terms: 4b(-4 + 3b)(-1 + 4b) = 0 Multiply (-4 + 3b) * (-1 + 4b) 4b(-4(-1 + 4b) + 3b * (-1 + 4b)) = 0 4b((-1 * -4 + 4b * -4) + 3b * (-1 + 4b)) = 0 4b((4 + -16b) + 3b * (-1 + 4b)) = 0 4b(4 + -16b + (-1 * 3b + 4b * 3b)) = 0 4b(4 + -16b + (-3b + 12b2)) = 0 Combine like terms: -16b + -3b = -19b 4b(4 + -19b + 12b2) = 0 (4 * 4b + -19b * 4b + 12b2 * 4b) = 0 (16b + -76b2 + 48b3) = 0 Solving 16b + -76b2 + 48b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4b'. 4b(4 + -19b + 12b2) = 0 Factor a trinomial. 4b((1 + -4b)(4 + -3b)) = 0 Ignore the factor 4.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 + -4b)' equal to zero and attempt to solve: Simplifying 1 + -4b = 0 Solving 1 + -4b = 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 + -4b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4b = 0 + -1 -4b = 0 + -1 Combine like terms: 0 + -1 = -1 -4b = -1 Divide each side by '-4'. b = 0.25 Simplifying b = 0.25Subproblem 3
Set the factor '(4 + -3b)' equal to zero and attempt to solve: Simplifying 4 + -3b = 0 Solving 4 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b = 0 + -4 -3b = 0 + -4 Combine like terms: 0 + -4 = -4 -3b = -4 Divide each side by '-3'. b = 1.333333333 Simplifying b = 1.333333333Solution
b = {0, 0.25, 1.333333333}
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