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Simplifying (a + -1ab)(3a + -2b) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 Multiply (a + -1ab) * (3a + -2b) (a(3a + -2b) + -1ab * (3a + -2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 ((3a * a + -2b * a) + -1ab * (3a + -2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 Reorder the terms: ((-2ab + 3a2) + -1ab * (3a + -2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 ((-2ab + 3a2) + -1ab * (3a + -2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 (-2ab + 3a2 + (3a * -1ab + -2b * -1ab)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 Reorder the terms: (-2ab + 3a2 + (2ab2 + -3a2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 (-2ab + 3a2 + (2ab2 + -3a2b)) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 Reorder the terms: (-2ab + 2ab2 + 3a2 + -3a2b) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 (-2ab + 2ab2 + 3a2 + -3a2b) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0 Multiply (a + -2b) * (3a + 2ab) -2ab + 2ab2 + 3a2 + -3a2b + -1(a(3a + 2ab) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + -1((3a * a + 2ab * a) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + -1((3a2 + 2a2b) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + -1(3a2 + 2a2b + (3a * -2b + 2ab * -2b)) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + -1(3a2 + 2a2b + (-6ab + -4ab2)) + -6ab(b + -1a) = 0 Reorder the terms: -2ab + 2ab2 + 3a2 + -3a2b + -1(-6ab + -4ab2 + 3a2 + 2a2b) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + -1(-6ab + -4ab2 + 3a2 + 2a2b) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + (-6ab * -1 + -4ab2 * -1 + 3a2 * -1 + 2a2b * -1) + -6ab(b + -1a) = 0 -2ab + 2ab2 + 3a2 + -3a2b + (6ab + 4ab2 + -3a2 + -2a2b) + -6ab(b + -1a) = 0 Reorder the terms: -2ab + 2ab2 + 3a2 + -3a2b + 6ab + 4ab2 + -3a2 + -2a2b + -6ab(-1a + b) = 0 -2ab + 2ab2 + 3a2 + -3a2b + 6ab + 4ab2 + -3a2 + -2a2b + (-1a * -6ab + b * -6ab) = 0 Reorder the terms: -2ab + 2ab2 + 3a2 + -3a2b + 6ab + 4ab2 + -3a2 + -2a2b + (-6ab2 + 6a2b) = 0 -2ab + 2ab2 + 3a2 + -3a2b + 6ab + 4ab2 + -3a2 + -2a2b + (-6ab2 + 6a2b) = 0 Reorder the terms: -2ab + 6ab + 2ab2 + 4ab2 + -6ab2 + 3a2 + -3a2 + -3a2b + -2a2b + 6a2b = 0 Combine like terms: -2ab + 6ab = 4ab 4ab + 2ab2 + 4ab2 + -6ab2 + 3a2 + -3a2 + -3a2b + -2a2b + 6a2b = 0 Combine like terms: 2ab2 + 4ab2 = 6ab2 4ab + 6ab2 + -6ab2 + 3a2 + -3a2 + -3a2b + -2a2b + 6a2b = 0 Combine like terms: 6ab2 + -6ab2 = 0 4ab + 0 + 3a2 + -3a2 + -3a2b + -2a2b + 6a2b = 0 4ab + 3a2 + -3a2 + -3a2b + -2a2b + 6a2b = 0 Combine like terms: 3a2 + -3a2 = 0 4ab + 0 + -3a2b + -2a2b + 6a2b = 0 4ab + -3a2b + -2a2b + 6a2b = 0 Combine like terms: -3a2b + -2a2b = -5a2b 4ab + -5a2b + 6a2b = 0 Combine like terms: -5a2b + 6a2b = 1a2b 4ab + 1a2b = 0 Solving 4ab + 1a2b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'ab'. ab(4 + a) = 0Subproblem 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 '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Solution
a = {-4}
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