(3x-2y)(5x-y)=

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Solution for (3x-2y)(5x-y)= equation: 


Simplifying
(3x + -2y)(5x + -1y) = 0

Multiply (3x + -2y) * (5x + -1y)
(3x * (5x + -1y) + -2y * (5x + -1y)) = 0
((5x * 3x + -1y * 3x) + -2y * (5x + -1y)) = 0

Reorder the terms:
((-3xy + 15x2) + -2y * (5x + -1y)) = 0
((-3xy + 15x2) + -2y * (5x + -1y)) = 0
(-3xy + 15x2 + (5x * -2y + -1y * -2y)) = 0
(-3xy + 15x2 + (-10xy + 2y2)) = 0

Reorder the terms:
(-3xy + -10xy + 15x2 + 2y2) = 0

Combine like terms: -3xy + -10xy = -13xy
(-13xy + 15x2 + 2y2) = 0

Solving
-13xy + 15x2 + 2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -2y)(5x + -1y) = 0


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 '(5x + -1y)' equal to zero and attempt to solve:

Simplifying
5x + -1y = 0

Solving
5x + -1y = 0

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

Add 'y' to each side of the equation.
5x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
5x + 0 = 0 + y
5x = 0 + y
Remove the zero:
5x = y

Divide each side by '5'.
x = 0.2y

Simplifying
x = 0.2y
Solution
x = {0.6666666667y, 0.2y}

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