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Simplifying (2b + 3)(3b + -4) = 0 Reorder the terms: (3 + 2b)(3b + -4) = 0 Reorder the terms: (3 + 2b)(-4 + 3b) = 0 Multiply (3 + 2b) * (-4 + 3b) (3(-4 + 3b) + 2b * (-4 + 3b)) = 0 ((-4 * 3 + 3b * 3) + 2b * (-4 + 3b)) = 0 ((-12 + 9b) + 2b * (-4 + 3b)) = 0 (-12 + 9b + (-4 * 2b + 3b * 2b)) = 0 (-12 + 9b + (-8b + 6b2)) = 0 Combine like terms: 9b + -8b = 1b (-12 + 1b + 6b2) = 0 Solving -12 + 1b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -2b)(4 + -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 '(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 = {-1.5, 1.333333333}
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