(5x+6y)(5x+6y)=0

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Solution for (5x+6y)(5x+6y)=0 equation: 


Simplifying
(5x + 6y)(5x + 6y) = 0

Multiply (5x + 6y) * (5x + 6y)
(5x * (5x + 6y) + 6y * (5x + 6y)) = 0
((5x * 5x + 6y * 5x) + 6y * (5x + 6y)) = 0

Reorder the terms:
((30xy + 25x2) + 6y * (5x + 6y)) = 0
((30xy + 25x2) + 6y * (5x + 6y)) = 0
(30xy + 25x2 + (5x * 6y + 6y * 6y)) = 0
(30xy + 25x2 + (30xy + 36y2)) = 0

Reorder the terms:
(30xy + 30xy + 25x2 + 36y2) = 0

Combine like terms: 30xy + 30xy = 60xy
(60xy + 25x2 + 36y2) = 0

Solving
60xy + 25x2 + 36y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 6y)(5x + 6y) = 0


Subproblem 1
Set the factor '(5x + 6y)' equal to zero and attempt to solve:

Simplifying
5x + 6y = 0

Solving
5x + 6y = 0

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

Add '-6y' to each side of the equation.
5x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
5x + 0 = 0 + -6y
5x = 0 + -6y
Remove the zero:
5x = -6y

Divide each side by '5'.
x = -1.2y

Simplifying
x = -1.2y

Subproblem 2
Set the factor '(5x + 6y)' equal to zero and attempt to solve:

Simplifying
5x + 6y = 0

Solving
5x + 6y = 0

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

Add '-6y' to each side of the equation.
5x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
5x + 0 = 0 + -6y
5x = 0 + -6y
Remove the zero:
5x = -6y

Divide each side by '5'.
x = -1.2y

Simplifying
x = -1.2y
Solution
x = {-1.2y, -1.2y}

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