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

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


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

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

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

Reorder the terms:
(-8xy + 3xy + 6x2 + -4y2) = 0

Combine like terms: -8xy + 3xy = -5xy
(-5xy + 6x2 + -4y2) = 0

Solving
-5xy + 6x2 + -4y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {1.333333333y, -0.5y}

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