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Simplifying (5b + 6)(3b + -4) = 0 Reorder the terms: (6 + 5b)(3b + -4) = 0 Reorder the terms: (6 + 5b)(-4 + 3b) = 0 Multiply (6 + 5b) * (-4 + 3b) (6(-4 + 3b) + 5b * (-4 + 3b)) = 0 ((-4 * 6 + 3b * 6) + 5b * (-4 + 3b)) = 0 ((-24 + 18b) + 5b * (-4 + 3b)) = 0 (-24 + 18b + (-4 * 5b + 3b * 5b)) = 0 (-24 + 18b + (-20b + 15b2)) = 0 Combine like terms: 18b + -20b = -2b (-24 + -2b + 15b2) = 0 Solving -24 + -2b + 15b2 = 0 Solving for variable 'b'. Factor a trinomial. (-6 + -5b)(4 + -3b) = 0Subproblem 1
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 = -1.2Subproblem 2
Set the factor '(4 + -3b)' equal to zero and attempt to solve: Simplifying 4 + -3b = 0 Solving 4 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b = 0 + -4 -3b = 0 + -4 Combine like terms: 0 + -4 = -4 -3b = -4 Divide each side by '-3'. b = 1.333333333 Simplifying b = 1.333333333Solution
b = {-1.2, 1.333333333}
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