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Simplifying 12a4 + -36a2b + 27b2 = 0 Reorder the terms: -36a2b + 12a4 + 27b2 = 0 Solving -36a2b + 12a4 + 27b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12a2b + 4a4 + 9b2) = 0 Factor a trinomial. 3((2a2 + -3b)(2a2 + -3b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2a2 + -3b)' equal to zero and attempt to solve: Simplifying 2a2 + -3b = 0 Solving 2a2 + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a2 + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a2 + 0 = 0 + 3b 2a2 = 0 + 3b Remove the zero: 2a2 = 3b Divide each side by '2'. a2 = 1.5b Simplifying a2 = 1.5b 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 '(2a2 + -3b)' equal to zero and attempt to solve: Simplifying 2a2 + -3b = 0 Solving 2a2 + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a2 + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a2 + 0 = 0 + 3b 2a2 = 0 + 3b Remove the zero: 2a2 = 3b Divide each side by '2'. a2 = 1.5b Simplifying a2 = 1.5b The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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