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Simplifying 6a2b + 9ab + -27b = 0 Reorder the terms: 9ab + 6a2b + -27b = 0 Solving 9ab + 6a2b + -27b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3b'. 3b(3a + 2a2 + -9) = 0 Factor a trinomial. 3b((2a + -3)(a + 3)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b = 0 + -1b Remove the zero: 0 = -1b Simplifying 0 = -1b The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2a + -3)' equal to zero and attempt to solve: Simplifying 2a + -3 = 0 Reorder the terms: -3 + 2a = 0 Solving -3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2a = 0 + 3 2a = 0 + 3 Combine like terms: 0 + 3 = 3 2a = 3 Divide each side by '2'. a = 1.5 Simplifying a = 1.5Subproblem 3
Set the factor '(a + 3)' equal to zero and attempt to solve: Simplifying a + 3 = 0 Reorder the terms: 3 + a = 0 Solving 3 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + a = 0 + -3 a = 0 + -3 Combine like terms: 0 + -3 = -3 a = -3 Simplifying a = -3Solution
a = {1.5, -3}
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