a*(3a-2b)-(a-2b)*(3a+2ab)-6ab(b-a)=

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Solution for a*(3a-2b)-(a-2b)*(3a+2ab)-6ab(b-a)= equation: 


Simplifying
a(3a + -2b) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0
(3a * a + -2b * a) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0

Reorder the terms:
(-2ab + 3a2) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0
(-2ab + 3a2) + -1(a + -2b)(3a + 2ab) + -6ab(b + -1a) = 0

Multiply (a + -2b) * (3a + 2ab)
-2ab + 3a2 + -1(a(3a + 2ab) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0
-2ab + 3a2 + -1((3a * a + 2ab * a) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0
-2ab + 3a2 + -1((3a2 + 2a2b) + -2b * (3a + 2ab)) + -6ab(b + -1a) = 0
-2ab + 3a2 + -1(3a2 + 2a2b + (3a * -2b + 2ab * -2b)) + -6ab(b + -1a) = 0
-2ab + 3a2 + -1(3a2 + 2a2b + (-6ab + -4ab2)) + -6ab(b + -1a) = 0

Reorder the terms:
-2ab + 3a2 + -1(-6ab + -4ab2 + 3a2 + 2a2b) + -6ab(b + -1a) = 0
-2ab + 3a2 + -1(-6ab + -4ab2 + 3a2 + 2a2b) + -6ab(b + -1a) = 0
-2ab + 3a2 + (-6ab * -1 + -4ab2 * -1 + 3a2 * -1 + 2a2b * -1) + -6ab(b + -1a) = 0
-2ab + 3a2 + (6ab + 4ab2 + -3a2 + -2a2b) + -6ab(b + -1a) = 0

Reorder the terms:
-2ab + 3a2 + 6ab + 4ab2 + -3a2 + -2a2b + -6ab(-1a + b) = 0
-2ab + 3a2 + 6ab + 4ab2 + -3a2 + -2a2b + (-1a * -6ab + b * -6ab) = 0

Reorder the terms:
-2ab + 3a2 + 6ab + 4ab2 + -3a2 + -2a2b + (-6ab2 + 6a2b) = 0
-2ab + 3a2 + 6ab + 4ab2 + -3a2 + -2a2b + (-6ab2 + 6a2b) = 0

Reorder the terms:
-2ab + 6ab + 4ab2 + -6ab2 + 3a2 + -3a2 + -2a2b + 6a2b = 0

Combine like terms: -2ab + 6ab = 4ab
4ab + 4ab2 + -6ab2 + 3a2 + -3a2 + -2a2b + 6a2b = 0

Combine like terms: 4ab2 + -6ab2 = -2ab2
4ab + -2ab2 + 3a2 + -3a2 + -2a2b + 6a2b = 0

Combine like terms: 3a2 + -3a2 = 0
4ab + -2ab2 + 0 + -2a2b + 6a2b = 0
4ab + -2ab2 + -2a2b + 6a2b = 0

Combine like terms: -2a2b + 6a2b = 4a2b
4ab + -2ab2 + 4a2b = 0

Solving
4ab + -2ab2 + 4a2b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2ab'.
2ab(2 + -1b + 2a) = 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 '(2 + -1b + 2a)' equal to zero and attempt to solve:

Simplifying
2 + -1b + 2a = 0

Reorder the terms:
2 + 2a + -1b = 0

Solving
2 + 2a + -1b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + 2a + -2 + -1b = 0 + -2

Reorder the terms:
2 + -2 + 2a + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2a + -1b = 0 + -2
2a + -1b = 0 + -2

Combine like terms: 0 + -2 = -2
2a + -1b = -2

Add 'b' to each side of the equation.
2a + -1b + b = -2 + b

Combine like terms: -1b + b = 0
2a + 0 = -2 + b
2a = -2 + b

Divide each side by '2'.
a = -1 + 0.5b

Simplifying
a = -1 + 0.5b
Solution
a = {-1 + 0.5b}

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