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Simplifying -27b2 + 27b + 30 = 0 Reorder the terms: 30 + 27b + -27b2 = 0 Solving 30 + 27b + -27b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 9b + -9b2) = 0 Factor a trinomial. 3((5 + -3b)(2 + 3b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Subproblem 2
Set the factor '(2 + 3b)' equal to zero and attempt to solve: Simplifying 2 + 3b = 0 Solving 2 + 3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3b = 0 + -2 3b = 0 + -2 Combine like terms: 0 + -2 = -2 3b = -2 Divide each side by '3'. b = -0.6666666667 Simplifying b = -0.6666666667Solution
b = {1.666666667, -0.6666666667}
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