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Simplifying (8b + 5)(3b + -5) = 0 Reorder the terms: (5 + 8b)(3b + -5) = 0 Reorder the terms: (5 + 8b)(-5 + 3b) = 0 Multiply (5 + 8b) * (-5 + 3b) (5(-5 + 3b) + 8b * (-5 + 3b)) = 0 ((-5 * 5 + 3b * 5) + 8b * (-5 + 3b)) = 0 ((-25 + 15b) + 8b * (-5 + 3b)) = 0 (-25 + 15b + (-5 * 8b + 3b * 8b)) = 0 (-25 + 15b + (-40b + 24b2)) = 0 Combine like terms: 15b + -40b = -25b (-25 + -25b + 24b2) = 0 Solving -25 + -25b + 24b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -8b)(5 + -3b) = 0Subproblem 1
Set the factor '(-5 + -8b)' equal to zero and attempt to solve: Simplifying -5 + -8b = 0 Solving -5 + -8b = 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 + -8b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8b = 0 + 5 -8b = 0 + 5 Combine like terms: 0 + 5 = 5 -8b = 5 Divide each side by '-8'. b = -0.625 Simplifying b = -0.625Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {-0.625, 1.666666667}
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