3x(x-4y)+4y(x-4y)=0

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Solution for 3x(x-4y)+4y(x-4y)=0 equation: 


Simplifying
3x(x + -4y) + 4y(x + -4y) = 0
(x * 3x + -4y * 3x) + 4y(x + -4y) = 0

Reorder the terms:
(-12xy + 3x2) + 4y(x + -4y) = 0
(-12xy + 3x2) + 4y(x + -4y) = 0
-12xy + 3x2 + (x * 4y + -4y * 4y) = 0
-12xy + 3x2 + (4xy + -16y2) = 0

Reorder the terms:
-12xy + 4xy + 3x2 + -16y2 = 0

Combine like terms: -12xy + 4xy = -8xy
-8xy + 3x2 + -16y2 = 0

Solving
-8xy + 3x2 + -16y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y

Subproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {4y, -1.333333333y}

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