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Simplifying 5(9b + -4)[3(4b + -2) + 3] = 0 Reorder the terms: 5(-4 + 9b)[3(4b + -2) + 3] = 0 Reorder the terms: 5(-4 + 9b)[3(-2 + 4b) + 3] = 0 5(-4 + 9b)[(-2 * 3 + 4b * 3) + 3] = 0 5(-4 + 9b)[(-6 + 12b) + 3] = 0 Reorder the terms: 5(-4 + 9b)[-6 + 3 + 12b] = 0 Combine like terms: -6 + 3 = -3 5(-4 + 9b)[-3 + 12b] = 0 Multiply (-4 + 9b) * [-3 + 12b] 5(-4[-3 + 12b] + 9b * [-3 + 12b]) = 0 5([-3 * -4 + 12b * -4] + 9b * [-3 + 12b]) = 0 5([12 + -48b] + 9b * [-3 + 12b]) = 0 5(12 + -48b + [-3 * 9b + 12b * 9b]) = 0 5(12 + -48b + [-27b + 108b2]) = 0 Combine like terms: -48b + -27b = -75b 5(12 + -75b + 108b2) = 0 (12 * 5 + -75b * 5 + 108b2 * 5) = 0 (60 + -375b + 540b2) = 0 Solving 60 + -375b + 540b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '15'. 15(4 + -25b + 36b2) = 0 Factor a trinomial. 15((1 + -4b)(4 + -9b)) = 0 Ignore the factor 15.Subproblem 1
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 2
Set the factor '(4 + -9b)' equal to zero and attempt to solve: Simplifying 4 + -9b = 0 Solving 4 + -9b = 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 + -9b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9b = 0 + -4 -9b = 0 + -4 Combine like terms: 0 + -4 = -4 -9b = -4 Divide each side by '-9'. b = 0.4444444444 Simplifying b = 0.4444444444Solution
b = {0.25, 0.4444444444}
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