4y(2y-3x)-2x(x-3y)=

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Solution for 4y(2y-3x)-2x(x-3y)= equation: 


Simplifying
4y(2y + -3x) + -2x(x + -3y) = 0

Reorder the terms:
4y(-3x + 2y) + -2x(x + -3y) = 0
(-3x * 4y + 2y * 4y) + -2x(x + -3y) = 0
(-12xy + 8y2) + -2x(x + -3y) = 0
-12xy + 8y2 + (x * -2x + -3y * -2x) = 0

Reorder the terms:
-12xy + 8y2 + (6xy + -2x2) = 0
-12xy + 8y2 + (6xy + -2x2) = 0

Reorder the terms:
-12xy + 6xy + -2x2 + 8y2 = 0

Combine like terms: -12xy + 6xy = -6xy
-6xy + -2x2 + 8y2 = 0

Solving
-6xy + -2x2 + 8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3xy + -1x2 + 4y2) = 0

Factor a trinomial.
2((-1x + -4y)(x + -1y)) = 0

Ignore the factor 2.

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

Simplifying
-1x + -4y = 0

Solving
-1x + -4y = 0

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

Add '4y' to each side of the equation.
-1x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
-1x + 0 = 0 + 4y
-1x = 0 + 4y
Remove the zero:
-1x = 4y

Divide each side by '-1'.
x = -4y

Simplifying
x = -4y

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

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

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