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Simplifying (9b + 5)(4b + -3) = 0 Reorder the terms: (5 + 9b)(4b + -3) = 0 Reorder the terms: (5 + 9b)(-3 + 4b) = 0 Multiply (5 + 9b) * (-3 + 4b) (5(-3 + 4b) + 9b * (-3 + 4b)) = 0 ((-3 * 5 + 4b * 5) + 9b * (-3 + 4b)) = 0 ((-15 + 20b) + 9b * (-3 + 4b)) = 0 (-15 + 20b + (-3 * 9b + 4b * 9b)) = 0 (-15 + 20b + (-27b + 36b2)) = 0 Combine like terms: 20b + -27b = -7b (-15 + -7b + 36b2) = 0 Solving -15 + -7b + 36b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -9b)(3 + -4b) = 0Subproblem 1
Set the factor '(-5 + -9b)' equal to zero and attempt to solve: Simplifying -5 + -9b = 0 Solving -5 + -9b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -9b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9b = 0 + 5 -9b = 0 + 5 Combine like terms: 0 + 5 = 5 -9b = 5 Divide each side by '-9'. b = -0.5555555556 Simplifying b = -0.5555555556Subproblem 2
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 = {-0.5555555556, 0.75}
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