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Simplifying (5b + -3)(6b + -8) = 0 Reorder the terms: (-3 + 5b)(6b + -8) = 0 Reorder the terms: (-3 + 5b)(-8 + 6b) = 0 Multiply (-3 + 5b) * (-8 + 6b) (-3(-8 + 6b) + 5b * (-8 + 6b)) = 0 ((-8 * -3 + 6b * -3) + 5b * (-8 + 6b)) = 0 ((24 + -18b) + 5b * (-8 + 6b)) = 0 (24 + -18b + (-8 * 5b + 6b * 5b)) = 0 (24 + -18b + (-40b + 30b2)) = 0 Combine like terms: -18b + -40b = -58b (24 + -58b + 30b2) = 0 Solving 24 + -58b + 30b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -29b + 15b2) = 0 Factor a trinomial. 2((3 + -5b)(4 + -3b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -5b)' equal to zero and attempt to solve: Simplifying 3 + -5b = 0 Solving 3 + -5b = 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 + -5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b = 0 + -3 -5b = 0 + -3 Combine like terms: 0 + -3 = -3 -5b = -3 Divide each side by '-5'. b = 0.6 Simplifying b = 0.6Subproblem 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 = {0.6, 1.333333333}
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