[2x-y][3x-y]=

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Solution for [2x-y][3x-y]= equation: 


Simplifying
[2x + -1y][3x + -1y] = 0

Multiply [2x + -1y] * [3x + -1y]
[2x * [3x + -1y] + -1y * [3x + -1y]] = 0
[[3x * 2x + -1y * 2x] + -1y * [3x + -1y]] = 0

Reorder the terms:
[[-2xy + 6x2] + -1y * [3x + -1y]] = 0
[[-2xy + 6x2] + -1y * [3x + -1y]] = 0
[-2xy + 6x2 + [3x * -1y + -1y * -1y]] = 0
[-2xy + 6x2 + [-3xy + 1y2]] = 0

Reorder the terms:
[-2xy + -3xy + 6x2 + 1y2] = 0

Combine like terms: -2xy + -3xy = -5xy
[-5xy + 6x2 + 1y2] = 0

Solving
-5xy + 6x2 + 1y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -1y)(3x + -1y) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
3x + -1y = 0

Solving
3x + -1y = 0

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

Add 'y' to each side of the equation.
3x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
3x + 0 = 0 + y
3x = 0 + y
Remove the zero:
3x = y

Divide each side by '3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {0.5y, 0.3333333333y}

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