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Simplifying (2b + -5)(5b + -8) = 0 Reorder the terms: (-5 + 2b)(5b + -8) = 0 Reorder the terms: (-5 + 2b)(-8 + 5b) = 0 Multiply (-5 + 2b) * (-8 + 5b) (-5(-8 + 5b) + 2b * (-8 + 5b)) = 0 ((-8 * -5 + 5b * -5) + 2b * (-8 + 5b)) = 0 ((40 + -25b) + 2b * (-8 + 5b)) = 0 (40 + -25b + (-8 * 2b + 5b * 2b)) = 0 (40 + -25b + (-16b + 10b2)) = 0 Combine like terms: -25b + -16b = -41b (40 + -41b + 10b2) = 0 Solving 40 + -41b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (8 + -5b)(5 + -2b) = 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 + -2b)' equal to zero and attempt to solve: Simplifying 5 + -2b = 0 Solving 5 + -2b = 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 + -2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2b = 0 + -5 -2b = 0 + -5 Combine like terms: 0 + -5 = -5 -2b = -5 Divide each side by '-2'. b = 2.5 Simplifying b = 2.5Solution
b = {1.6, 2.5}
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