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Simplifying (4b + 3)(b + -2) = 0 Reorder the terms: (3 + 4b)(b + -2) = 0 Reorder the terms: (3 + 4b)(-2 + b) = 0 Multiply (3 + 4b) * (-2 + b) (3(-2 + b) + 4b * (-2 + b)) = 0 ((-2 * 3 + b * 3) + 4b * (-2 + b)) = 0 ((-6 + 3b) + 4b * (-2 + b)) = 0 (-6 + 3b + (-2 * 4b + b * 4b)) = 0 (-6 + 3b + (-8b + 4b2)) = 0 Combine like terms: 3b + -8b = -5b (-6 + -5b + 4b2) = 0 Solving -6 + -5b + 4b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -4b)(2 + -1b) = 0Subproblem 1
Set the factor '(-3 + -4b)' equal to zero and attempt to solve: Simplifying -3 + -4b = 0 Solving -3 + -4b = 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 + -4b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4b = 0 + 3 -4b = 0 + 3 Combine like terms: 0 + 3 = 3 -4b = 3 Divide each side by '-4'. b = -0.75 Simplifying b = -0.75Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve: Simplifying 2 + -1b = 0 Solving 2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1b = 0 + -2 -1b = 0 + -2 Combine like terms: 0 + -2 = -2 -1b = -2 Divide each side by '-1'. b = 2 Simplifying b = 2Solution
b = {-0.75, 2}
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