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Simplifying (5b + 3)(2b + -3) = 0 Reorder the terms: (3 + 5b)(2b + -3) = 0 Reorder the terms: (3 + 5b)(-3 + 2b) = 0 Multiply (3 + 5b) * (-3 + 2b) (3(-3 + 2b) + 5b * (-3 + 2b)) = 0 ((-3 * 3 + 2b * 3) + 5b * (-3 + 2b)) = 0 ((-9 + 6b) + 5b * (-3 + 2b)) = 0 (-9 + 6b + (-3 * 5b + 2b * 5b)) = 0 (-9 + 6b + (-15b + 10b2)) = 0 Combine like terms: 6b + -15b = -9b (-9 + -9b + 10b2) = 0 Solving -9 + -9b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -5b)(3 + -2b) = 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 '(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 = 1.5Solution
b = {-0.6, 1.5}
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