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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 = -35b (8 + -35b + 12b2) = 0 Solving 8 + -35b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (1 + -4b)(8 + -3b) = 0Subproblem 1
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 = 0.25Subproblem 2
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 = 2.666666667Solution
b = {0.25, 2.666666667}
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