(3x+2y)(4x-2y)=0

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Solution for (3x+2y)(4x-2y)=0 equation: 


Simplifying
(3x + 2y)(4x + -2y) = 0

Multiply (3x + 2y) * (4x + -2y)
(3x * (4x + -2y) + 2y * (4x + -2y)) = 0
((4x * 3x + -2y * 3x) + 2y * (4x + -2y)) = 0

Reorder the terms:
((-6xy + 12x2) + 2y * (4x + -2y)) = 0
((-6xy + 12x2) + 2y * (4x + -2y)) = 0
(-6xy + 12x2 + (4x * 2y + -2y * 2y)) = 0
(-6xy + 12x2 + (8xy + -4y2)) = 0

Reorder the terms:
(-6xy + 8xy + 12x2 + -4y2) = 0

Combine like terms: -6xy + 8xy = 2xy
(2xy + 12x2 + -4y2) = 0

Solving
2xy + 12x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + 6x2 + -2y2) = 0

Factor a trinomial.
2((2x + -1y)(3x + 2y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

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

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y
Solution
x = {0.5y, -0.6666666667y}

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