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Simplifying (5b + 3)(5b + -8) = 0 Reorder the terms: (3 + 5b)(5b + -8) = 0 Reorder the terms: (3 + 5b)(-8 + 5b) = 0 Multiply (3 + 5b) * (-8 + 5b) (3(-8 + 5b) + 5b * (-8 + 5b)) = 0 ((-8 * 3 + 5b * 3) + 5b * (-8 + 5b)) = 0 ((-24 + 15b) + 5b * (-8 + 5b)) = 0 (-24 + 15b + (-8 * 5b + 5b * 5b)) = 0 (-24 + 15b + (-40b + 25b2)) = 0 Combine like terms: 15b + -40b = -25b (-24 + -25b + 25b2) = 0 Solving -24 + -25b + 25b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -5b)(8 + -5b) = 0Subproblem 1
Set the factor '(-3 + -5b)' equal to zero and attempt to solve: Simplifying -3 + -5b = 0 Solving -3 + -5b = 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 + -5b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5b = 0 + 3 -5b = 0 + 3 Combine like terms: 0 + 3 = 3 -5b = 3 Divide each side by '-5'. b = -0.6 Simplifying b = -0.6Subproblem 2
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 = 1.6Solution
b = {-0.6, 1.6}
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