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Simplifying (6b + -5)(8b + 3) = 0 Reorder the terms: (-5 + 6b)(8b + 3) = 0 Reorder the terms: (-5 + 6b)(3 + 8b) = 0 Multiply (-5 + 6b) * (3 + 8b) (-5(3 + 8b) + 6b * (3 + 8b)) = 0 ((3 * -5 + 8b * -5) + 6b * (3 + 8b)) = 0 ((-15 + -40b) + 6b * (3 + 8b)) = 0 (-15 + -40b + (3 * 6b + 8b * 6b)) = 0 (-15 + -40b + (18b + 48b2)) = 0 Combine like terms: -40b + 18b = -22b (-15 + -22b + 48b2) = 0 Solving -15 + -22b + 48b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -8b)(5 + -6b) = 0Subproblem 1
Set the factor '(-3 + -8b)' equal to zero and attempt to solve: Simplifying -3 + -8b = 0 Solving -3 + -8b = 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 + -8b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8b = 0 + 3 -8b = 0 + 3 Combine like terms: 0 + 3 = 3 -8b = 3 Divide each side by '-8'. b = -0.375 Simplifying b = -0.375Subproblem 2
Set the factor '(5 + -6b)' equal to zero and attempt to solve: Simplifying 5 + -6b = 0 Solving 5 + -6b = 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 + -6b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6b = 0 + -5 -6b = 0 + -5 Combine like terms: 0 + -5 = -5 -6b = -5 Divide each side by '-6'. b = 0.8333333333 Simplifying b = 0.8333333333Solution
b = {-0.375, 0.8333333333}
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