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Simplifying (8b + 3)(5b + -15) = 0 Reorder the terms: (3 + 8b)(5b + -15) = 0 Reorder the terms: (3 + 8b)(-15 + 5b) = 0 Multiply (3 + 8b) * (-15 + 5b) (3(-15 + 5b) + 8b * (-15 + 5b)) = 0 ((-15 * 3 + 5b * 3) + 8b * (-15 + 5b)) = 0 ((-45 + 15b) + 8b * (-15 + 5b)) = 0 (-45 + 15b + (-15 * 8b + 5b * 8b)) = 0 (-45 + 15b + (-120b + 40b2)) = 0 Combine like terms: 15b + -120b = -105b (-45 + -105b + 40b2) = 0 Solving -45 + -105b + 40b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -21b + 8b2) = 0 Factor a trinomial. 5((-3 + -8b)(3 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -8b)' equal to zero and attempt to solve: Simplifying -3 + -8b = 0 Solving -3 + -8b = 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 + -8b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8b = 0 + 3 -8b = 0 + 3 Combine like terms: 0 + 3 = 3 -8b = 3 Divide each side by '-8'. b = -0.375 Simplifying b = -0.375Subproblem 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 = {-0.375, 3}
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