(10x+10y)(10x+10y)=

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Solution for (10x+10y)(10x+10y)= equation: 


Simplifying
(10x + 10y)(10x + 10y) = 0

Multiply (10x + 10y) * (10x + 10y)
(10x * (10x + 10y) + 10y * (10x + 10y)) = 0
((10x * 10x + 10y * 10x) + 10y * (10x + 10y)) = 0

Reorder the terms:
((100xy + 100x2) + 10y * (10x + 10y)) = 0
((100xy + 100x2) + 10y * (10x + 10y)) = 0
(100xy + 100x2 + (10x * 10y + 10y * 10y)) = 0
(100xy + 100x2 + (100xy + 100y2)) = 0

Reorder the terms:
(100xy + 100xy + 100x2 + 100y2) = 0

Combine like terms: 100xy + 100xy = 200xy
(200xy + 100x2 + 100y2) = 0

Solving
200xy + 100x2 + 100y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '100'.
100(2xy + x2 + y2) = 0

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

Ignore the factor 100.

Subproblem 1
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y

Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {-1y, -1y}

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