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

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


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

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

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

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

Combine like terms: 25xy + 4xy = 29xy
(29xy + 10x2 + 10y2) = 0

Solving
29xy + 10x2 + 10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 2y)(2x + 5y) = 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 '(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 = {-0.4y, -2.5y}

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