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Simplifying (8b + 1)(b + -3) = 0 Reorder the terms: (1 + 8b)(b + -3) = 0 Reorder the terms: (1 + 8b)(-3 + b) = 0 Multiply (1 + 8b) * (-3 + b) (1(-3 + b) + 8b * (-3 + b)) = 0 ((-3 * 1 + b * 1) + 8b * (-3 + b)) = 0 ((-3 + 1b) + 8b * (-3 + b)) = 0 (-3 + 1b + (-3 * 8b + b * 8b)) = 0 (-3 + 1b + (-24b + 8b2)) = 0 Combine like terms: 1b + -24b = -23b (-3 + -23b + 8b2) = 0 Solving -3 + -23b + 8b2 = 0 Solving for variable 'b'. Factor a trinomial. (-1 + -8b)(3 + -1b) = 0Subproblem 1
Set the factor '(-1 + -8b)' equal to zero and attempt to solve: Simplifying -1 + -8b = 0 Solving -1 + -8b = 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 + -8b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8b = 0 + 1 -8b = 0 + 1 Combine like terms: 0 + 1 = 1 -8b = 1 Divide each side by '-8'. b = -0.125 Simplifying b = -0.125Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-0.125, 3}
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