(75x+27y)(75x+27y)=0

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Solution for (75x+27y)(75x+27y)=0 equation: 


Simplifying
(75x + 27y)(75x + 27y) = 0

Multiply (75x + 27y) * (75x + 27y)
(75x * (75x + 27y) + 27y * (75x + 27y)) = 0
((75x * 75x + 27y * 75x) + 27y * (75x + 27y)) = 0

Reorder the terms:
((2025xy + 5625x2) + 27y * (75x + 27y)) = 0
((2025xy + 5625x2) + 27y * (75x + 27y)) = 0
(2025xy + 5625x2 + (75x * 27y + 27y * 27y)) = 0
(2025xy + 5625x2 + (2025xy + 729y2)) = 0

Reorder the terms:
(2025xy + 2025xy + 5625x2 + 729y2) = 0

Combine like terms: 2025xy + 2025xy = 4050xy
(4050xy + 5625x2 + 729y2) = 0

Solving
4050xy + 5625x2 + 729y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(450xy + 625x2 + 81y2) = 0

Factor a trinomial.
9((25x + 9y)(25x + 9y)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(25x + 9y)' equal to zero and attempt to solve:

Simplifying
25x + 9y = 0

Solving
25x + 9y = 0

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

Add '-9y' to each side of the equation.
25x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
25x + 0 = 0 + -9y
25x = 0 + -9y
Remove the zero:
25x = -9y

Divide each side by '25'.
x = -0.36y

Simplifying
x = -0.36y

Subproblem 2
Set the factor '(25x + 9y)' equal to zero and attempt to solve:

Simplifying
25x + 9y = 0

Solving
25x + 9y = 0

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

Add '-9y' to each side of the equation.
25x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
25x + 0 = 0 + -9y
25x = 0 + -9y
Remove the zero:
25x = -9y

Divide each side by '25'.
x = -0.36y

Simplifying
x = -0.36y
Solution
x = {-0.36y, -0.36y}

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