(4x-2y)(3x-5y)=

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Solution for (4x-2y)(3x-5y)= equation: 


Simplifying
(4x + -2y)(3x + -5y) = 0

Multiply (4x + -2y) * (3x + -5y)
(4x * (3x + -5y) + -2y * (3x + -5y)) = 0
((3x * 4x + -5y * 4x) + -2y * (3x + -5y)) = 0

Reorder the terms:
((-20xy + 12x2) + -2y * (3x + -5y)) = 0
((-20xy + 12x2) + -2y * (3x + -5y)) = 0
(-20xy + 12x2 + (3x * -2y + -5y * -2y)) = 0
(-20xy + 12x2 + (-6xy + 10y2)) = 0

Reorder the terms:
(-20xy + -6xy + 12x2 + 10y2) = 0

Combine like terms: -20xy + -6xy = -26xy
(-26xy + 12x2 + 10y2) = 0

Solving
-26xy + 12x2 + 10y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13xy + 6x2 + 5y2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -5y)' equal to zero and attempt to solve:

Simplifying
3x + -5y = 0

Solving
3x + -5y = 0

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

Add '5y' to each side of the equation.
3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
3x + 0 = 0 + 5y
3x = 0 + 5y
Remove the zero:
3x = 5y

Divide each side by '3'.
x = 1.666666667y

Simplifying
x = 1.666666667y

Subproblem 2
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
Solution
x = {1.666666667y, 0.5y}

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