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Simplifying (5b + -12)(2b + 9) = 0 Reorder the terms: (-12 + 5b)(2b + 9) = 0 Reorder the terms: (-12 + 5b)(9 + 2b) = 0 Multiply (-12 + 5b) * (9 + 2b) (-12(9 + 2b) + 5b * (9 + 2b)) = 0 ((9 * -12 + 2b * -12) + 5b * (9 + 2b)) = 0 ((-108 + -24b) + 5b * (9 + 2b)) = 0 (-108 + -24b + (9 * 5b + 2b * 5b)) = 0 (-108 + -24b + (45b + 10b2)) = 0 Combine like terms: -24b + 45b = 21b (-108 + 21b + 10b2) = 0 Solving -108 + 21b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (-9 + -2b)(12 + -5b) = 0Subproblem 1
Set the factor '(-9 + -2b)' equal to zero and attempt to solve: Simplifying -9 + -2b = 0 Solving -9 + -2b = 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 + -2b = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2b = 0 + 9 -2b = 0 + 9 Combine like terms: 0 + 9 = 9 -2b = 9 Divide each side by '-2'. b = -4.5 Simplifying b = -4.5Subproblem 2
Set the factor '(12 + -5b)' equal to zero and attempt to solve: Simplifying 12 + -5b = 0 Solving 12 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5b = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5b = 0 + -12 -5b = 0 + -12 Combine like terms: 0 + -12 = -12 -5b = -12 Divide each side by '-5'. b = 2.4 Simplifying b = 2.4Solution
b = {-4.5, 2.4}
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