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Simplifying (2b + -3)(b + 9) = 0 Reorder the terms: (-3 + 2b)(b + 9) = 0 Reorder the terms: (-3 + 2b)(9 + b) = 0 Multiply (-3 + 2b) * (9 + b) (-3(9 + b) + 2b * (9 + b)) = 0 ((9 * -3 + b * -3) + 2b * (9 + b)) = 0 ((-27 + -3b) + 2b * (9 + b)) = 0 (-27 + -3b + (9 * 2b + b * 2b)) = 0 (-27 + -3b + (18b + 2b2)) = 0 Combine like terms: -3b + 18b = 15b (-27 + 15b + 2b2) = 0 Solving -27 + 15b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (-9 + -1b)(3 + -2b) = 0Subproblem 1
Set the factor '(-9 + -1b)' equal to zero and attempt to solve: Simplifying -9 + -1b = 0 Solving -9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1b = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1b = 0 + 9 -1b = 0 + 9 Combine like terms: 0 + 9 = 9 -1b = 9 Divide each side by '-1'. b = -9 Simplifying b = -9Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Solution
b = {-9, 1.5}
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