(2x+4y)(4x+6y)=0

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Solution for (2x+4y)(4x+6y)=0 equation: 


Simplifying
(2x + 4y)(4x + 6y) = 0

Multiply (2x + 4y) * (4x + 6y)
(2x * (4x + 6y) + 4y * (4x + 6y)) = 0
((4x * 2x + 6y * 2x) + 4y * (4x + 6y)) = 0

Reorder the terms:
((12xy + 8x2) + 4y * (4x + 6y)) = 0
((12xy + 8x2) + 4y * (4x + 6y)) = 0
(12xy + 8x2 + (4x * 4y + 6y * 4y)) = 0
(12xy + 8x2 + (16xy + 24y2)) = 0

Reorder the terms:
(12xy + 16xy + 8x2 + 24y2) = 0

Combine like terms: 12xy + 16xy = 28xy
(28xy + 8x2 + 24y2) = 0

Solving
28xy + 8x2 + 24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7xy + 2x2 + 6y2) = 0

Factor a trinomial.
4((2x + 3y)(x + 2y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2x + 3y)' equal to zero and attempt to solve:

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

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

Simplifying
x + 2y = 0

Solving
x + 2y = 0

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

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

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

Simplifying
x = -2y
Solution
x = {-1.5y, -2y}

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