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Simplifying (5b + -1)(6b + 3) = 0 Reorder the terms: (-1 + 5b)(6b + 3) = 0 Reorder the terms: (-1 + 5b)(3 + 6b) = 0 Multiply (-1 + 5b) * (3 + 6b) (-1(3 + 6b) + 5b * (3 + 6b)) = 0 ((3 * -1 + 6b * -1) + 5b * (3 + 6b)) = 0 ((-3 + -6b) + 5b * (3 + 6b)) = 0 (-3 + -6b + (3 * 5b + 6b * 5b)) = 0 (-3 + -6b + (15b + 30b2)) = 0 Combine like terms: -6b + 15b = 9b (-3 + 9b + 30b2) = 0 Solving -3 + 9b + 30b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 3b + 10b2) = 0 Factor a trinomial. 3((-1 + -2b)(1 + -5b)) = 0 Ignore the factor 3.Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(1 + -5b)' equal to zero and attempt to solve: Simplifying 1 + -5b = 0 Solving 1 + -5b = 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 + -5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5b = 0 + -1 -5b = 0 + -1 Combine like terms: 0 + -1 = -1 -5b = -1 Divide each side by '-5'. b = 0.2 Simplifying b = 0.2Solution
b = {-0.5, 0.2}
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