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

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


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

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

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

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

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

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

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

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

Solving
-1xy + -2x2 + 10y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-2x + -5y)' equal to zero and attempt to solve:

Simplifying
-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

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 = {-2.5y, 2y}

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