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Simplifying (-7b + 5)(4b + -3) = 0 Reorder the terms: (5 + -7b)(4b + -3) = 0 Reorder the terms: (5 + -7b)(-3 + 4b) = 0 Multiply (5 + -7b) * (-3 + 4b) (5(-3 + 4b) + -7b * (-3 + 4b)) = 0 ((-3 * 5 + 4b * 5) + -7b * (-3 + 4b)) = 0 ((-15 + 20b) + -7b * (-3 + 4b)) = 0 (-15 + 20b + (-3 * -7b + 4b * -7b)) = 0 (-15 + 20b + (21b + -28b2)) = 0 Combine like terms: 20b + 21b = 41b (-15 + 41b + -28b2) = 0 Solving -15 + 41b + -28b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + 4b)(5 + -7b) = 0Subproblem 1
Set the factor '(-3 + 4b)' equal to zero and attempt to solve: Simplifying -3 + 4b = 0 Solving -3 + 4b = 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 + 4b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4b = 0 + 3 4b = 0 + 3 Combine like terms: 0 + 3 = 3 4b = 3 Divide each side by '4'. b = 0.75 Simplifying b = 0.75Subproblem 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 = {0.75, 0.7142857143}
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