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Simplifying (4b + -1)(3b + 8) = 0 Reorder the terms: (-1 + 4b)(3b + 8) = 0 Reorder the terms: (-1 + 4b)(8 + 3b) = 0 Multiply (-1 + 4b) * (8 + 3b) (-1(8 + 3b) + 4b * (8 + 3b)) = 0 ((8 * -1 + 3b * -1) + 4b * (8 + 3b)) = 0 ((-8 + -3b) + 4b * (8 + 3b)) = 0 (-8 + -3b + (8 * 4b + 3b * 4b)) = 0 (-8 + -3b + (32b + 12b2)) = 0 Combine like terms: -3b + 32b = 29b (-8 + 29b + 12b2) = 0 Solving -8 + 29b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (-8 + -3b)(1 + -4b) = 0Subproblem 1
Set the factor '(-8 + -3b)' equal to zero and attempt to solve: Simplifying -8 + -3b = 0 Solving -8 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3b = 0 + 8 -3b = 0 + 8 Combine like terms: 0 + 8 = 8 -3b = 8 Divide each side by '-3'. b = -2.666666667 Simplifying b = -2.666666667Subproblem 2
Set the factor '(1 + -4b)' equal to zero and attempt to solve: Simplifying 1 + -4b = 0 Solving 1 + -4b = 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 + -4b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4b = 0 + -1 -4b = 0 + -1 Combine like terms: 0 + -1 = -1 -4b = -1 Divide each side by '-4'. b = 0.25 Simplifying b = 0.25Solution
b = {-2.666666667, 0.25}
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