(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(-1xy + 6x2 + -2y2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

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

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