(x+6y)(5x+2y)=0

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Solution for (x+6y)(5x+2y)=0 equation: 


Simplifying
(x + 6y)(5x + 2y) = 0

Multiply (x + 6y) * (5x + 2y)
(x(5x + 2y) + 6y * (5x + 2y)) = 0
((5x * x + 2y * x) + 6y * (5x + 2y)) = 0

Reorder the terms:
((2xy + 5x2) + 6y * (5x + 2y)) = 0
((2xy + 5x2) + 6y * (5x + 2y)) = 0
(2xy + 5x2 + (5x * 6y + 2y * 6y)) = 0
(2xy + 5x2 + (30xy + 12y2)) = 0

Reorder the terms:
(2xy + 30xy + 5x2 + 12y2) = 0

Combine like terms: 2xy + 30xy = 32xy
(32xy + 5x2 + 12y2) = 0

Solving
32xy + 5x2 + 12y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 2y)(x + 6y) = 0


Subproblem 1
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

Add '-2y' to each side of the equation.
5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
5x + 0 = 0 + -2y
5x = 0 + -2y
Remove the zero:
5x = -2y

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y

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

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

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

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

Simplifying
x = -6y
Solution
x = {-0.4y, -6y}

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