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

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


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

Reorder the terms:
(-3x + 2y)(5y + -2x) = 0

Reorder the terms:
(-3x + 2y)(-2x + 5y) = 0

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

Reorder the terms:
((-15xy + 6x2) + 2y * (-2x + 5y)) = 0
((-15xy + 6x2) + 2y * (-2x + 5y)) = 0
(-15xy + 6x2 + (-2x * 2y + 5y * 2y)) = 0
(-15xy + 6x2 + (-4xy + 10y2)) = 0

Reorder the terms:
(-15xy + -4xy + 6x2 + 10y2) = 0

Combine like terms: -15xy + -4xy = -19xy
(-19xy + 6x2 + 10y2) = 0

Solving
-19xy + 6x2 + 10y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y

Subproblem 2
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
Solution
x = {2.5y, 0.6666666667y}

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