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

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


Simplifying
(3x + 4y)(2x + -1y) = 0

Multiply (3x + 4y) * (2x + -1y)
(3x * (2x + -1y) + 4y * (2x + -1y)) = 0
((2x * 3x + -1y * 3x) + 4y * (2x + -1y)) = 0

Reorder the terms:
((-3xy + 6x2) + 4y * (2x + -1y)) = 0
((-3xy + 6x2) + 4y * (2x + -1y)) = 0
(-3xy + 6x2 + (2x * 4y + -1y * 4y)) = 0
(-3xy + 6x2 + (8xy + -4y2)) = 0

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

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

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

Solving for variable 'x'.

Factor a trinomial.
(2x + -1y)(3x + 4y) = 0


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 + 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 = {0.5y, -1.333333333y}

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