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Simplifying (4b)(3b2 + 2b + -1) = 0 Remove parenthesis around (4b) 4b(3b2 + 2b + -1) = 0 Reorder the terms: 4b(-1 + 2b + 3b2) = 0 (-1 * 4b + 2b * 4b + 3b2 * 4b) = 0 (-4b + 8b2 + 12b3) = 0 Solving -4b + 8b2 + 12b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4b'. 4b(-1 + 2b + 3b2) = 0 Factor a trinomial. 4b((-1 + -1b)(1 + -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 + -1b)' equal to zero and attempt to solve: Simplifying -1 + -1b = 0 Solving -1 + -1b = 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 + -1b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1b = 0 + 1 -1b = 0 + 1 Combine like terms: 0 + 1 = 1 -1b = 1 Divide each side by '-1'. b = -1 Simplifying b = -1Subproblem 3
Set the factor '(1 + -3b)' equal to zero and attempt to solve: Simplifying 1 + -3b = 0 Solving 1 + -3b = 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 + -3b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3b = 0 + -1 -3b = 0 + -1 Combine like terms: 0 + -1 = -1 -3b = -1 Divide each side by '-3'. b = 0.3333333333 Simplifying b = 0.3333333333Solution
b = {0, -1, 0.3333333333}
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