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Simplifying 6ab3 + -14a2b2 + 4a3b = 0 Solving 6ab3 + -14a2b2 + 4a3b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2ab'. 2ab(3b2 + -7ab + 2a2) = 0 Factor a trinomial. 2ab((b + -2a)(3b + -1a)) = 0 Ignore the factor 2.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 + -2a)' equal to zero and attempt to solve: Simplifying b + -2a = 0 Reorder the terms: -2a + b = 0 Solving -2a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -2a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -2a + 0 = 0 + -1b -2a = 0 + -1b Remove the zero: -2a = -1b Divide each side by '-2'. a = 0.5b Simplifying a = 0.5bSubproblem 3
Set the factor '(3b + -1a)' equal to zero and attempt to solve: Simplifying 3b + -1a = 0 Reorder the terms: -1a + 3b = 0 Solving -1a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. -1a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 -1a + 0 = 0 + -3b -1a = 0 + -3b Remove the zero: -1a = -3b Divide each side by '-1'. a = 3b Simplifying a = 3bSolution
a = {0.5b, 3b}
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