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

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


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

Reorder the terms:
(4x + -3y)(-2x + 5y) = 0

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

Reorder the terms:
((20xy + -8x2) + -3y * (-2x + 5y)) = 0
((20xy + -8x2) + -3y * (-2x + 5y)) = 0
(20xy + -8x2 + (-2x * -3y + 5y * -3y)) = 0
(20xy + -8x2 + (6xy + -15y2)) = 0

Reorder the terms:
(20xy + 6xy + -8x2 + -15y2) = 0

Combine like terms: 20xy + 6xy = 26xy
(26xy + -8x2 + -15y2) = 0

Solving
26xy + -8x2 + -15y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4x + 3y)(2x + -5y) = 0


Subproblem 1
Set the factor '(-4x + 3y)' equal to zero and attempt to solve:

Simplifying
-4x + 3y = 0

Solving
-4x + 3y = 0

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

Add '-3y' to each side of the equation.
-4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
-4x + 0 = 0 + -3y
-4x = 0 + -3y
Remove the zero:
-4x = -3y

Divide each side by '-4'.
x = 0.75y

Simplifying
x = 0.75y

Subproblem 2
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
Solution
x = {0.75y, 2.5y}

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