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Simplifying (2b + -5)(2b + 6) = 0 Reorder the terms: (-5 + 2b)(2b + 6) = 0 Reorder the terms: (-5 + 2b)(6 + 2b) = 0 Multiply (-5 + 2b) * (6 + 2b) (-5(6 + 2b) + 2b * (6 + 2b)) = 0 ((6 * -5 + 2b * -5) + 2b * (6 + 2b)) = 0 ((-30 + -10b) + 2b * (6 + 2b)) = 0 (-30 + -10b + (6 * 2b + 2b * 2b)) = 0 (-30 + -10b + (12b + 4b2)) = 0 Combine like terms: -10b + 12b = 2b (-30 + 2b + 4b2) = 0 Solving -30 + 2b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + b + 2b2) = 0 Factor a trinomial. 2((-3 + -1b)(5 + -2b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 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 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 2
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 = 2.5Solution
b = {-3, 2.5}
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