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Simplifying (3b + 13)(5b + -6) = 0 Reorder the terms: (13 + 3b)(5b + -6) = 0 Reorder the terms: (13 + 3b)(-6 + 5b) = 0 Multiply (13 + 3b) * (-6 + 5b) (13(-6 + 5b) + 3b * (-6 + 5b)) = 0 ((-6 * 13 + 5b * 13) + 3b * (-6 + 5b)) = 0 ((-78 + 65b) + 3b * (-6 + 5b)) = 0 (-78 + 65b + (-6 * 3b + 5b * 3b)) = 0 (-78 + 65b + (-18b + 15b2)) = 0 Combine like terms: 65b + -18b = 47b (-78 + 47b + 15b2) = 0 Solving -78 + 47b + 15b2 = 0 Solving for variable 'b'. Factor a trinomial. (-13 + -3b)(6 + -5b) = 0Subproblem 1
Set the factor '(-13 + -3b)' equal to zero and attempt to solve: Simplifying -13 + -3b = 0 Solving -13 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -3b = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3b = 0 + 13 -3b = 0 + 13 Combine like terms: 0 + 13 = 13 -3b = 13 Divide each side by '-3'. b = -4.333333333 Simplifying b = -4.333333333Subproblem 2
Set the factor '(6 + -5b)' equal to zero and attempt to solve: Simplifying 6 + -5b = 0 Solving 6 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5b = 0 + -6 -5b = 0 + -6 Combine like terms: 0 + -6 = -6 -5b = -6 Divide each side by '-5'. b = 1.2 Simplifying b = 1.2Solution
b = {-4.333333333, 1.2}
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