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Simplifying (3b + -5)(4b + -5) = 0 Reorder the terms: (-5 + 3b)(4b + -5) = 0 Reorder the terms: (-5 + 3b)(-5 + 4b) = 0 Multiply (-5 + 3b) * (-5 + 4b) (-5(-5 + 4b) + 3b * (-5 + 4b)) = 0 ((-5 * -5 + 4b * -5) + 3b * (-5 + 4b)) = 0 ((25 + -20b) + 3b * (-5 + 4b)) = 0 (25 + -20b + (-5 * 3b + 4b * 3b)) = 0 (25 + -20b + (-15b + 12b2)) = 0 Combine like terms: -20b + -15b = -35b (25 + -35b + 12b2) = 0 Solving 25 + -35b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (5 + -4b)(5 + -3b) = 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 '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {1.25, 1.666666667}
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