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Simplifying 6b3 + 37b2 + 45b = 0 Reorder the terms: 45b + 37b2 + 6b3 = 0 Solving 45b + 37b2 + 6b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b'. b(45 + 37b + 6b2) = 0 Factor a trinomial. b((9 + 2b)(5 + 3b)) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(9 + 2b)' equal to zero and attempt to solve: Simplifying 9 + 2b = 0 Solving 9 + 2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2b = 0 + -9 2b = 0 + -9 Combine like terms: 0 + -9 = -9 2b = -9 Divide each side by '2'. b = -4.5 Simplifying b = -4.5Subproblem 3
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 = -1.666666667Solution
b = {0, -4.5, -1.666666667}
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