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

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


Simplifying
(3x + 2y) * x(3x + -2y) + -1yx(x + -4y) = 0

Reorder the terms for easier multiplication:
x(3x + 2y)(3x + -2y) + -1yx(x + -4y) = 0

Multiply (3x + 2y) * (3x + -2y)
x(3x * (3x + -2y) + 2y * (3x + -2y)) + -1yx(x + -4y) = 0
x((3x * 3x + -2y * 3x) + 2y * (3x + -2y)) + -1yx(x + -4y) = 0

Reorder the terms:
x((-6xy + 9x2) + 2y * (3x + -2y)) + -1yx(x + -4y) = 0
x((-6xy + 9x2) + 2y * (3x + -2y)) + -1yx(x + -4y) = 0
x(-6xy + 9x2 + (3x * 2y + -2y * 2y)) + -1yx(x + -4y) = 0
x(-6xy + 9x2 + (6xy + -4y2)) + -1yx(x + -4y) = 0

Reorder the terms:
x(-6xy + 6xy + 9x2 + -4y2) + -1yx(x + -4y) = 0

Combine like terms: -6xy + 6xy = 0
x(0 + 9x2 + -4y2) + -1yx(x + -4y) = 0
x(9x2 + -4y2) + -1yx(x + -4y) = 0
(9x2 * x + -4y2 * x) + -1yx(x + -4y) = 0

Reorder the terms:
(-4xy2 + 9x3) + -1yx(x + -4y) = 0
(-4xy2 + 9x3) + -1yx(x + -4y) = 0
-4xy2 + 9x3 + (x * -1xy + -4y * -1xy) = 0

Reorder the terms:
-4xy2 + 9x3 + (4xy2 + -1x2y) = 0
-4xy2 + 9x3 + (4xy2 + -1x2y) = 0

Reorder the terms:
-4xy2 + 4xy2 + -1x2y + 9x3 = 0

Combine like terms: -4xy2 + 4xy2 = 0
0 + -1x2y + 9x3 = 0
-1x2y + 9x3 = 0

Solving
-1x2y + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1y + 9x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-1y + 9x)' equal to zero and attempt to solve:

Simplifying
-1y + 9x = 0

Reorder the terms:
9x + -1y = 0

Solving
9x + -1y = 0

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

Add 'y' to each side of the equation.
9x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
9x + 0 = 0 + y
9x = 0 + y
Remove the zero:
9x = y

Divide each side by '9'.
x = 0.1111111111y

Simplifying
x = 0.1111111111y
Solution
x = {0, 0.1111111111y}

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