(5x-2y)(5x-2y)=0

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Solution for (5x-2y)(5x-2y)=0 equation: 


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

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

Reorder the terms:
((-10xy + 25x2) + -2y * (5x + -2y)) = 0
((-10xy + 25x2) + -2y * (5x + -2y)) = 0
(-10xy + 25x2 + (5x * -2y + -2y * -2y)) = 0
(-10xy + 25x2 + (-10xy + 4y2)) = 0

Reorder the terms:
(-10xy + -10xy + 25x2 + 4y2) = 0

Combine like terms: -10xy + -10xy = -20xy
(-20xy + 25x2 + 4y2) = 0

Solving
-20xy + 25x2 + 4y2 = 0

Solving for variable 'x'.

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


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 + -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
Solution
x = {0.4y, 0.4y}

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