(5x-2y)(10x+2y)=

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Solution for (5x-2y)(10x+2y)= equation: 


Simplifying
(5x + -2y)(10x + 2y) = 0

Multiply (5x + -2y) * (10x + 2y)
(5x * (10x + 2y) + -2y * (10x + 2y)) = 0
((10x * 5x + 2y * 5x) + -2y * (10x + 2y)) = 0

Reorder the terms:
((10xy + 50x2) + -2y * (10x + 2y)) = 0
((10xy + 50x2) + -2y * (10x + 2y)) = 0
(10xy + 50x2 + (10x * -2y + 2y * -2y)) = 0
(10xy + 50x2 + (-20xy + -4y2)) = 0

Reorder the terms:
(10xy + -20xy + 50x2 + -4y2) = 0

Combine like terms: 10xy + -20xy = -10xy
(-10xy + 50x2 + -4y2) = 0

Solving
-10xy + 50x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5xy + 25x2 + -2y2) = 0

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

Ignore the factor 2.

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

Simplifying
5x + -2y = 0

Solving
5x + -2y = 0

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

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

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

Divide each side by '5'.
x = 0.4y

Simplifying
x = 0.4y

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

Simplifying
5x + y = 0

Solving
5x + y = 0

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

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

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

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

Simplifying
x = -0.2y
Solution
x = {0.4y, -0.2y}

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