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Simplifying (3b + -5)(2b + -3) = 0 Reorder the terms: (-5 + 3b)(2b + -3) = 0 Reorder the terms: (-5 + 3b)(-3 + 2b) = 0 Multiply (-5 + 3b) * (-3 + 2b) (-5(-3 + 2b) + 3b * (-3 + 2b)) = 0 ((-3 * -5 + 2b * -5) + 3b * (-3 + 2b)) = 0 ((15 + -10b) + 3b * (-3 + 2b)) = 0 (15 + -10b + (-3 * 3b + 2b * 3b)) = 0 (15 + -10b + (-9b + 6b2)) = 0 Combine like terms: -10b + -9b = -19b (15 + -19b + 6b2) = 0 Solving 15 + -19b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -2b)(5 + -3b) = 0Subproblem 1
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {1.5, 1.666666667}
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