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Simplifying 9b(4b + -3)(3b + 4) = 0 Reorder the terms: 9b(-3 + 4b)(3b + 4) = 0 Reorder the terms: 9b(-3 + 4b)(4 + 3b) = 0 Multiply (-3 + 4b) * (4 + 3b) 9b(-3(4 + 3b) + 4b * (4 + 3b)) = 0 9b((4 * -3 + 3b * -3) + 4b * (4 + 3b)) = 0 9b((-12 + -9b) + 4b * (4 + 3b)) = 0 9b(-12 + -9b + (4 * 4b + 3b * 4b)) = 0 9b(-12 + -9b + (16b + 12b2)) = 0 Combine like terms: -9b + 16b = 7b 9b(-12 + 7b + 12b2) = 0 (-12 * 9b + 7b * 9b + 12b2 * 9b) = 0 (-108b + 63b2 + 108b3) = 0 Solving -108b + 63b2 + 108b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '9b'. 9b(-12 + 7b + 12b2) = 0 Factor a trinomial. 9b((-4 + -3b)(3 + -4b)) = 0 Ignore the factor 9.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 '(-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 = -1.333333333Subproblem 3
Set the factor '(3 + -4b)' equal to zero and attempt to solve: Simplifying 3 + -4b = 0 Solving 3 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4b = 0 + -3 -4b = 0 + -3 Combine like terms: 0 + -3 = -3 -4b = -3 Divide each side by '-4'. b = 0.75 Simplifying b = 0.75Solution
b = {0, -1.333333333, 0.75}
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