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Simplifying (7b + -5)(8b + 7) = 0 Reorder the terms: (-5 + 7b)(8b + 7) = 0 Reorder the terms: (-5 + 7b)(7 + 8b) = 0 Multiply (-5 + 7b) * (7 + 8b) (-5(7 + 8b) + 7b * (7 + 8b)) = 0 ((7 * -5 + 8b * -5) + 7b * (7 + 8b)) = 0 ((-35 + -40b) + 7b * (7 + 8b)) = 0 (-35 + -40b + (7 * 7b + 8b * 7b)) = 0 (-35 + -40b + (49b + 56b2)) = 0 Combine like terms: -40b + 49b = 9b (-35 + 9b + 56b2) = 0 Solving -35 + 9b + 56b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -8b)(5 + -7b) = 0Subproblem 1
Set the factor '(-7 + -8b)' equal to zero and attempt to solve: Simplifying -7 + -8b = 0 Solving -7 + -8b = 0 Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -8b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8b = 0 + 7 -8b = 0 + 7 Combine like terms: 0 + 7 = 7 -8b = 7 Divide each side by '-8'. b = -0.875 Simplifying b = -0.875Subproblem 2
Set the factor '(5 + -7b)' equal to zero and attempt to solve: Simplifying 5 + -7b = 0 Solving 5 + -7b = 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 + -7b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7b = 0 + -5 -7b = 0 + -5 Combine like terms: 0 + -5 = -5 -7b = -5 Divide each side by '-7'. b = 0.7142857143 Simplifying b = 0.7142857143Solution
b = {-0.875, 0.7142857143}
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