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Simplifying (6b + 3)(-1b + -4) = 0 Reorder the terms: (3 + 6b)(-1b + -4) = 0 Reorder the terms: (3 + 6b)(-4 + -1b) = 0 Multiply (3 + 6b) * (-4 + -1b) (3(-4 + -1b) + 6b * (-4 + -1b)) = 0 ((-4 * 3 + -1b * 3) + 6b * (-4 + -1b)) = 0 ((-12 + -3b) + 6b * (-4 + -1b)) = 0 (-12 + -3b + (-4 * 6b + -1b * 6b)) = 0 (-12 + -3b + (-24b + -6b2)) = 0 Combine like terms: -3b + -24b = -27b (-12 + -27b + -6b2) = 0 Solving -12 + -27b + -6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-3'. -3(4 + 9b + 2b2) = 0 Factor a trinomial. -3((4 + b)(1 + 2b)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(4 + b)' equal to zero and attempt to solve: Simplifying 4 + b = 0 Solving 4 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + b = 0 + -4 b = 0 + -4 Combine like terms: 0 + -4 = -4 b = -4 Simplifying b = -4Subproblem 2
Set the factor '(1 + 2b)' equal to zero and attempt to solve: Simplifying 1 + 2b = 0 Solving 1 + 2b = 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 + 2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2b = 0 + -1 2b = 0 + -1 Combine like terms: 0 + -1 = -1 2b = -1 Divide each side by '2'. b = -0.5 Simplifying b = -0.5Solution
b = {-4, -0.5}
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