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Simplifying (3b + -2)(b + 4) = 0 Reorder the terms: (-2 + 3b)(b + 4) = 0 Reorder the terms: (-2 + 3b)(4 + b) = 0 Multiply (-2 + 3b) * (4 + b) (-2(4 + b) + 3b * (4 + b)) = 0 ((4 * -2 + b * -2) + 3b * (4 + b)) = 0 ((-8 + -2b) + 3b * (4 + b)) = 0 (-8 + -2b + (4 * 3b + b * 3b)) = 0 (-8 + -2b + (12b + 3b2)) = 0 Combine like terms: -2b + 12b = 10b (-8 + 10b + 3b2) = 0 Solving -8 + 10b + 3b2 = 0 Solving for variable 'b'. Factor a trinomial. (-4 + -1b)(2 + -3b) = 0Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve: Simplifying -4 + -1b = 0 Solving -4 + -1b = 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 + -1b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1b = 0 + 4 -1b = 0 + 4 Combine like terms: 0 + 4 = 4 -1b = 4 Divide each side by '-1'. b = -4 Simplifying b = -4Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 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 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667Solution
b = {-4, 0.6666666667}
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