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

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


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

Reorder the terms for easier multiplication:
x(4x + -2y)(5x + -5y) = 0

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

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

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

Combine like terms: -20xy + -10xy = -30xy
x(-30xy + 20x2 + 10y2) = 0
(-30xy * x + 20x2 * x + 10y2 * x) = 0

Reorder the terms:
(10xy2 + -30x2y + 20x3) = 0
(10xy2 + -30x2y + 20x3) = 0

Solving
10xy2 + -30x2y + 20x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(y2 + -3xy + 2x2) = 0

Factor a trinomial.
10x((y + -2x)(y + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
y + -2x = 0

Reorder the terms:
-2x + y = 0

Solving
-2x + y = 0

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

Add '-1y' to each side of the equation.
-2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-2x + 0 = 0 + -1y
-2x = 0 + -1y
Remove the zero:
-2x = -1y

Divide each side by '-2'.
x = 0.5y

Simplifying
x = 0.5y

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

Simplifying
y + -1x = 0

Reorder the terms:
-1x + y = 0

Solving
-1x + y = 0

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

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

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

Divide each side by '-1'.
x = y

Simplifying
x = y
Solution
x = {0, 0.5y, y}

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