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

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


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

Reorder the terms:
(5x + y)(y + 5x) = 0

Reorder the terms:
(5x + y)(5x + y) = 0

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

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

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

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

Solving
10xy + 25x2 + y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-0.2y, -0.2y}

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