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

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


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

Combine like terms: 3x + -4x = -1x
(-1x + 2y) * x(2y + 3y + 2x) = 0

Reorder the terms:
(-1x + 2y) * x(2x + 2y + 3y) = 0

Combine like terms: 2y + 3y = 5y
(-1x + 2y) * x(2x + 5y) = 0

Reorder the terms for easier multiplication:
x(-1x + 2y)(2x + 5y) = 0

Multiply (-1x + 2y) * (2x + 5y)
x(-1x * (2x + 5y) + 2y * (2x + 5y)) = 0
x((2x * -1x + 5y * -1x) + 2y * (2x + 5y)) = 0

Reorder the terms:
x((-5xy + -2x2) + 2y * (2x + 5y)) = 0
x((-5xy + -2x2) + 2y * (2x + 5y)) = 0
x(-5xy + -2x2 + (2x * 2y + 5y * 2y)) = 0
x(-5xy + -2x2 + (4xy + 10y2)) = 0

Reorder the terms:
x(-5xy + 4xy + -2x2 + 10y2) = 0

Combine like terms: -5xy + 4xy = -1xy
x(-1xy + -2x2 + 10y2) = 0
(-1xy * x + -2x2 * x + 10y2 * x) = 0

Reorder the terms:
(10xy2 + -1x2y + -2x3) = 0
(10xy2 + -1x2y + -2x3) = 0

Solving
10xy2 + -1x2y + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10y2 + -1xy + -2x2) = 0

Factor a trinomial.
x((2y + -1x)(5y + 2x)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2y + -1x = 0

Reorder the terms:
-1x + 2y = 0

Solving
-1x + 2y = 0

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

Add '-2y' to each side of the equation.
-1x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-1x + 0 = 0 + -2y
-1x = 0 + -2y
Remove the zero:
-1x = -2y

Divide each side by '-1'.
x = 2y

Simplifying
x = 2y

Subproblem 3
Set the factor '(5y + 2x)' equal to zero and attempt to solve:

Simplifying
5y + 2x = 0

Reorder the terms:
2x + 5y = 0

Solving
2x + 5y = 0

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

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

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

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {0, 2y, -2.5y}

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