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Simplifying (4b + -5)(b + -4) = 0 Reorder the terms: (-5 + 4b)(b + -4) = 0 Reorder the terms: (-5 + 4b)(-4 + b) = 0 Multiply (-5 + 4b) * (-4 + b) (-5(-4 + b) + 4b * (-4 + b)) = 0 ((-4 * -5 + b * -5) + 4b * (-4 + b)) = 0 ((20 + -5b) + 4b * (-4 + b)) = 0 (20 + -5b + (-4 * 4b + b * 4b)) = 0 (20 + -5b + (-16b + 4b2)) = 0 Combine like terms: -5b + -16b = -21b (20 + -21b + 4b2) = 0 Solving 20 + -21b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (5 + -4b)(4 + -1b) = 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 '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {1.25, 4}
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