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Simplifying (5b + -2)(8b + 5) = 0 Reorder the terms: (-2 + 5b)(8b + 5) = 0 Reorder the terms: (-2 + 5b)(5 + 8b) = 0 Multiply (-2 + 5b) * (5 + 8b) (-2(5 + 8b) + 5b * (5 + 8b)) = 0 ((5 * -2 + 8b * -2) + 5b * (5 + 8b)) = 0 ((-10 + -16b) + 5b * (5 + 8b)) = 0 (-10 + -16b + (5 * 5b + 8b * 5b)) = 0 (-10 + -16b + (25b + 40b2)) = 0 Combine like terms: -16b + 25b = 9b (-10 + 9b + 40b2) = 0 Solving -10 + 9b + 40b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -8b)(2 + -5b) = 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 '(2 + -5b)' equal to zero and attempt to solve: Simplifying 2 + -5b = 0 Solving 2 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5b = 0 + -2 -5b = 0 + -2 Combine like terms: 0 + -2 = -2 -5b = -2 Divide each side by '-5'. b = 0.4 Simplifying b = 0.4Solution
b = {-0.625, 0.4}
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