=3x(2x-3y+2)

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Solution for =3x(2x-3y+2) equation: 


Simplifying
0 = 3x(2x + -3y + 2)

Reorder the terms:
0 = 3x(2 + 2x + -3y)
0 = (2 * 3x + 2x * 3x + -3y * 3x)

Reorder the terms:
0 = (6x + -9xy + 6x2)
0 = (6x + -9xy + 6x2)

Solving
0 = 6x + -9xy + 6x2

Solving for variable 'x'.
Remove the zero:
-6x + 9xy + -6x2 = 6x + -9xy + 6x2 + -6x + 9xy + -6x2

Reorder the terms:
-6x + 9xy + -6x2 = 6x + -6x + -9xy + 9xy + 6x2 + -6x2

Combine like terms: 6x + -6x = 0
-6x + 9xy + -6x2 = 0 + -9xy + 9xy + 6x2 + -6x2
-6x + 9xy + -6x2 = -9xy + 9xy + 6x2 + -6x2

Combine like terms: -9xy + 9xy = 0
-6x + 9xy + -6x2 = 0 + 6x2 + -6x2
-6x + 9xy + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-6x + 9xy + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-2 + 3y + -2x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-2 + 3y + -2x)' equal to zero and attempt to solve:

Simplifying
-2 + 3y + -2x = 0

Reorder the terms:
-2 + -2x + 3y = 0

Solving
-2 + -2x + 3y = 0

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

Add '2' to each side of the equation.
-2 + -2x + 2 + 3y = 0 + 2

Reorder the terms:
-2 + 2 + -2x + 3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2x + 3y = 0 + 2
-2x + 3y = 0 + 2

Combine like terms: 0 + 2 = 2
-2x + 3y = 2

Add '-3y' to each side of the equation.
-2x + 3y + -3y = 2 + -3y

Combine like terms: 3y + -3y = 0
-2x + 0 = 2 + -3y
-2x = 2 + -3y

Divide each side by '-2'.
x = -1 + 1.5y

Simplifying
x = -1 + 1.5y
Solution
x = {0, -1 + 1.5y}

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