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Simplifying (8b + -2)(-2b + 5) = 0 Reorder the terms: (-2 + 8b)(-2b + 5) = 0 Reorder the terms: (-2 + 8b)(5 + -2b) = 0 Multiply (-2 + 8b) * (5 + -2b) (-2(5 + -2b) + 8b * (5 + -2b)) = 0 ((5 * -2 + -2b * -2) + 8b * (5 + -2b)) = 0 ((-10 + 4b) + 8b * (5 + -2b)) = 0 (-10 + 4b + (5 * 8b + -2b * 8b)) = 0 (-10 + 4b + (40b + -16b2)) = 0 Combine like terms: 4b + 40b = 44b (-10 + 44b + -16b2) = 0 Solving -10 + 44b + -16b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 22b + -8b2) = 0 Factor a trinomial. 2((-5 + 2b)(1 + -4b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 2b)' equal to zero and attempt to solve: Simplifying -5 + 2b = 0 Solving -5 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2b = 0 + 5 2b = 0 + 5 Combine like terms: 0 + 5 = 5 2b = 5 Divide each side by '2'. b = 2.5 Simplifying b = 2.5Subproblem 2
Set the factor '(1 + -4b)' equal to zero and attempt to solve: Simplifying 1 + -4b = 0 Solving 1 + -4b = 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 + -4b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4b = 0 + -1 -4b = 0 + -1 Combine like terms: 0 + -1 = -1 -4b = -1 Divide each side by '-4'. b = 0.25 Simplifying b = 0.25Solution
b = {2.5, 0.25}
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