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

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


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

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

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

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

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

Solving
20xy + 4x2 + 25y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-2.5y, -2.5y}

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