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

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


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

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

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

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

Combine like terms: 2xy + 25xy = 27xy
(27xy + 5x2 + 10y2) = 0

Solving
27xy + 5x2 + 10y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 2y)(x + 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 '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {-0.4y, -5y}

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