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Simplifying (4b + -3)(b + 5) = 0 Reorder the terms: (-3 + 4b)(b + 5) = 0 Reorder the terms: (-3 + 4b)(5 + b) = 0 Multiply (-3 + 4b) * (5 + b) (-3(5 + b) + 4b * (5 + b)) = 0 ((5 * -3 + b * -3) + 4b * (5 + b)) = 0 ((-15 + -3b) + 4b * (5 + b)) = 0 (-15 + -3b + (5 * 4b + b * 4b)) = 0 (-15 + -3b + (20b + 4b2)) = 0 Combine like terms: -3b + 20b = 17b (-15 + 17b + 4b2) = 0 Solving -15 + 17b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -1b)(3 + -4b) = 0Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve: Simplifying -5 + -1b = 0 Solving -5 + -1b = 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 + -1b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b = 0 + 5 -1b = 0 + 5 Combine like terms: 0 + 5 = 5 -1b = 5 Divide each side by '-1'. b = -5 Simplifying b = -5Subproblem 2
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 = 0.75Solution
b = {-5, 0.75}
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