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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 = 3b (-35 + 3b + 20b2) = 0 Solving -35 + 3b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -5b)(5 + -4b) = 0Subproblem 1
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 = -1.4Subproblem 2
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 = 1.25Solution
b = {-1.4, 1.25}
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