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Simplifying (4b + -3)(5b + -5) = 0 Reorder the terms: (-3 + 4b)(5b + -5) = 0 Reorder the terms: (-3 + 4b)(-5 + 5b) = 0 Multiply (-3 + 4b) * (-5 + 5b) (-3(-5 + 5b) + 4b * (-5 + 5b)) = 0 ((-5 * -3 + 5b * -3) + 4b * (-5 + 5b)) = 0 ((15 + -15b) + 4b * (-5 + 5b)) = 0 (15 + -15b + (-5 * 4b + 5b * 4b)) = 0 (15 + -15b + (-20b + 20b2)) = 0 Combine like terms: -15b + -20b = -35b (15 + -35b + 20b2) = 0 Solving 15 + -35b + 20b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -7b + 4b2) = 0 Factor a trinomial. 5((3 + -4b)(1 + -1b)) = 0 Ignore the factor 5.Subproblem 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 '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 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 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {0.75, 1}
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