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

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


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

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

Reorder the terms:
((8xy + 6x2) + -3y * (3x + 4y)) = 0
((8xy + 6x2) + -3y * (3x + 4y)) = 0
(8xy + 6x2 + (3x * -3y + 4y * -3y)) = 0
(8xy + 6x2 + (-9xy + -12y2)) = 0

Reorder the terms:
(8xy + -9xy + 6x2 + -12y2) = 0

Combine like terms: 8xy + -9xy = -1xy
(-1xy + 6x2 + -12y2) = 0

Solving
-1xy + 6x2 + -12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -3y)(3x + 4y) = 0


Subproblem 1
Set the factor '(2x + -3y)' equal to zero and attempt to solve:

Simplifying
2x + -3y = 0

Solving
2x + -3y = 0

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

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

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

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y

Subproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {1.5y, -1.333333333y}

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