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Simplifying (5b + -3)(6b + -5) = 0 Reorder the terms: (-3 + 5b)(6b + -5) = 0 Reorder the terms: (-3 + 5b)(-5 + 6b) = 0 Multiply (-3 + 5b) * (-5 + 6b) (-3(-5 + 6b) + 5b * (-5 + 6b)) = 0 ((-5 * -3 + 6b * -3) + 5b * (-5 + 6b)) = 0 ((15 + -18b) + 5b * (-5 + 6b)) = 0 (15 + -18b + (-5 * 5b + 6b * 5b)) = 0 (15 + -18b + (-25b + 30b2)) = 0 Combine like terms: -18b + -25b = -43b (15 + -43b + 30b2) = 0 Solving 15 + -43b + 30b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -5b)(5 + -6b) = 0Subproblem 1
Set the factor '(3 + -5b)' equal to zero and attempt to solve: Simplifying 3 + -5b = 0 Solving 3 + -5b = 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 + -5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b = 0 + -3 -5b = 0 + -3 Combine like terms: 0 + -3 = -3 -5b = -3 Divide each side by '-5'. b = 0.6 Simplifying b = 0.6Subproblem 2
Set the factor '(5 + -6b)' equal to zero and attempt to solve: Simplifying 5 + -6b = 0 Solving 5 + -6b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6b = 0 + -5 -6b = 0 + -5 Combine like terms: 0 + -5 = -5 -6b = -5 Divide each side by '-6'. b = 0.8333333333 Simplifying b = 0.8333333333Solution
b = {0.6, 0.8333333333}
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