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Simplifying (-5b + 7)(-4b + 5) = 0 Reorder the terms: (7 + -5b)(-4b + 5) = 0 Reorder the terms: (7 + -5b)(5 + -4b) = 0 Multiply (7 + -5b) * (5 + -4b) (7(5 + -4b) + -5b * (5 + -4b)) = 0 ((5 * 7 + -4b * 7) + -5b * (5 + -4b)) = 0 ((35 + -28b) + -5b * (5 + -4b)) = 0 (35 + -28b + (5 * -5b + -4b * -5b)) = 0 (35 + -28b + (-25b + 20b2)) = 0 Combine like terms: -28b + -25b = -53b (35 + -53b + 20b2) = 0 Solving 35 + -53b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (5 + -4b)(7 + -5b) = 0Subproblem 1
Set the factor '(5 + -4b)' equal to zero and attempt to solve: Simplifying 5 + -4b = 0 Solving 5 + -4b = 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 + -4b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4b = 0 + -5 -4b = 0 + -5 Combine like terms: 0 + -5 = -5 -4b = -5 Divide each side by '-4'. b = 1.25 Simplifying b = 1.25Subproblem 2
Set the factor '(7 + -5b)' equal to zero and attempt to solve: Simplifying 7 + -5b = 0 Solving 7 + -5b = 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 + -5b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5b = 0 + -7 -5b = 0 + -7 Combine like terms: 0 + -7 = -7 -5b = -7 Divide each side by '-5'. b = 1.4 Simplifying b = 1.4Solution
b = {1.25, 1.4}
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