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Simplifying (8b + -6)(6b + -4) = 0 Reorder the terms: (-6 + 8b)(6b + -4) = 0 Reorder the terms: (-6 + 8b)(-4 + 6b) = 0 Multiply (-6 + 8b) * (-4 + 6b) (-6(-4 + 6b) + 8b * (-4 + 6b)) = 0 ((-4 * -6 + 6b * -6) + 8b * (-4 + 6b)) = 0 ((24 + -36b) + 8b * (-4 + 6b)) = 0 (24 + -36b + (-4 * 8b + 6b * 8b)) = 0 (24 + -36b + (-32b + 48b2)) = 0 Combine like terms: -36b + -32b = -68b (24 + -68b + 48b2) = 0 Solving 24 + -68b + 48b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -17b + 12b2) = 0 Factor a trinomial. 4((2 + -3b)(3 + -4b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667Subproblem 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 = {0.6666666667, 0.75}
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