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Simplifying (4b + -3)(5b + -1) = 0 Reorder the terms: (-3 + 4b)(5b + -1) = 0 Reorder the terms: (-3 + 4b)(-1 + 5b) = 0 Multiply (-3 + 4b) * (-1 + 5b) (-3(-1 + 5b) + 4b * (-1 + 5b)) = 0 ((-1 * -3 + 5b * -3) + 4b * (-1 + 5b)) = 0 ((3 + -15b) + 4b * (-1 + 5b)) = 0 (3 + -15b + (-1 * 4b + 5b * 4b)) = 0 (3 + -15b + (-4b + 20b2)) = 0 Combine like terms: -15b + -4b = -19b (3 + -19b + 20b2) = 0 Solving 3 + -19b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (1 + -5b)(3 + -4b) = 0Subproblem 1
Set the factor '(1 + -5b)' equal to zero and attempt to solve: Simplifying 1 + -5b = 0 Solving 1 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5b = 0 + -1 -5b = 0 + -1 Combine like terms: 0 + -1 = -1 -5b = -1 Divide each side by '-5'. b = 0.2 Simplifying b = 0.2Subproblem 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 = {0.2, 0.75}
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