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Simplifying 12a3b + -27a2b2 + 6ab3 = 0 Reorder the terms: 6ab3 + -27a2b2 + 12a3b = 0 Solving 6ab3 + -27a2b2 + 12a3b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3ab'. 3ab(2b2 + -9ab + 4a2) = 0 Factor a trinomial. 3ab((b + -4a)(2b + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve: Simplifying ab = 0 Solving ab = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ab = 0 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 '(b + -4a)' equal to zero and attempt to solve: Simplifying b + -4a = 0 Reorder the terms: -4a + b = 0 Solving -4a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -4a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -4a + 0 = 0 + -1b -4a = 0 + -1b Remove the zero: -4a = -1b Divide each side by '-4'. a = 0.25b Simplifying a = 0.25bSubproblem 3
Set the factor '(2b + -1a)' equal to zero and attempt to solve: Simplifying 2b + -1a = 0 Reorder the terms: -1a + 2b = 0 Solving -1a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. -1a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 -1a + 0 = 0 + -2b -1a = 0 + -2b Remove the zero: -1a = -2b Divide each side by '-1'. a = 2b Simplifying a = 2bSolution
a = {0.25b, 2b}
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