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Simplifying (4b + -2)(b + 4) = 0 Reorder the terms: (-2 + 4b)(b + 4) = 0 Reorder the terms: (-2 + 4b)(4 + b) = 0 Multiply (-2 + 4b) * (4 + b) (-2(4 + b) + 4b * (4 + b)) = 0 ((4 * -2 + b * -2) + 4b * (4 + b)) = 0 ((-8 + -2b) + 4b * (4 + b)) = 0 (-8 + -2b + (4 * 4b + b * 4b)) = 0 (-8 + -2b + (16b + 4b2)) = 0 Combine like terms: -2b + 16b = 14b (-8 + 14b + 4b2) = 0 Solving -8 + 14b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7b + 2b2) = 0 Factor a trinomial. 2((-4 + -1b)(1 + -2b)) = 0 Ignore the factor 2.Subproblem 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 '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Solution
b = {-4, 0.5}
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