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Simplifying (b + -4)(2b + -5) = 0 Reorder the terms: (-4 + b)(2b + -5) = 0 Reorder the terms: (-4 + b)(-5 + 2b) = 0 Multiply (-4 + b) * (-5 + 2b) (-4(-5 + 2b) + b(-5 + 2b)) = 0 ((-5 * -4 + 2b * -4) + b(-5 + 2b)) = 0 ((20 + -8b) + b(-5 + 2b)) = 0 (20 + -8b + (-5 * b + 2b * b)) = 0 (20 + -8b + (-5b + 2b2)) = 0 Combine like terms: -8b + -5b = -13b (20 + -13b + 2b2) = 0 Solving 20 + -13b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (5 + -2b)(4 + -1b) = 0Subproblem 1
Set the factor '(5 + -2b)' equal to zero and attempt to solve: Simplifying 5 + -2b = 0 Solving 5 + -2b = 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 + -2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2b = 0 + -5 -2b = 0 + -5 Combine like terms: 0 + -5 = -5 -2b = -5 Divide each side by '-2'. b = 2.5 Simplifying b = 2.5Subproblem 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 = {2.5, 4}
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