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Simplifying 6b2 + 54b + 120 = 0 Reorder the terms: 120 + 54b + 6b2 = 0 Solving 120 + 54b + 6b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '6'. 6(20 + 9b + b2) = 0 Factor a trinomial. 6((5 + b)(4 + b)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve: Simplifying 5 + b = 0 Solving 5 + b = 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 + b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + b = 0 + -5 b = 0 + -5 Combine like terms: 0 + -5 = -5 b = -5 Simplifying b = -5Subproblem 2
Set the factor '(4 + b)' equal to zero and attempt to solve: Simplifying 4 + b = 0 Solving 4 + b = 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 + b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + b = 0 + -4 b = 0 + -4 Combine like terms: 0 + -4 = -4 b = -4 Simplifying b = -4Solution
b = {-5, -4}
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