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Simplifying (4b + -5)(5b + 8) = 0 Reorder the terms: (-5 + 4b)(5b + 8) = 0 Reorder the terms: (-5 + 4b)(8 + 5b) = 0 Multiply (-5 + 4b) * (8 + 5b) (-5(8 + 5b) + 4b * (8 + 5b)) = 0 ((8 * -5 + 5b * -5) + 4b * (8 + 5b)) = 0 ((-40 + -25b) + 4b * (8 + 5b)) = 0 (-40 + -25b + (8 * 4b + 5b * 4b)) = 0 (-40 + -25b + (32b + 20b2)) = 0 Combine like terms: -25b + 32b = 7b (-40 + 7b + 20b2) = 0 Solving -40 + 7b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (-8 + -5b)(5 + -4b) = 0Subproblem 1
Set the factor '(-8 + -5b)' equal to zero and attempt to solve: Simplifying -8 + -5b = 0 Solving -8 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5b = 0 + 8 -5b = 0 + 8 Combine like terms: 0 + 8 = 8 -5b = 8 Divide each side by '-5'. b = -1.6 Simplifying b = -1.6Subproblem 2
Set the factor '(5 + -4b)' equal to zero and attempt to solve: Simplifying 5 + -4b = 0 Solving 5 + -4b = 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 + -4b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4b = 0 + -5 -4b = 0 + -5 Combine like terms: 0 + -5 = -5 -4b = -5 Divide each side by '-4'. b = 1.25 Simplifying b = 1.25Solution
b = {-1.6, 1.25}
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