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

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


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

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

Multiply (x + 2y) * (2x + 3y)
x(x(2x + 3y) + 2y * (2x + 3y)) = 0
x((2x * x + 3y * x) + 2y * (2x + 3y)) = 0

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

Reorder the terms:
x(3xy + 4xy + 2x2 + 6y2) = 0

Combine like terms: 3xy + 4xy = 7xy
x(7xy + 2x2 + 6y2) = 0
(7xy * x + 2x2 * x + 6y2 * x) = 0

Reorder the terms:
(6xy2 + 7x2y + 2x3) = 0
(6xy2 + 7x2y + 2x3) = 0

Solving
6xy2 + 7x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6y2 + 7xy + 2x2) = 0

Factor a trinomial.
x((2y + x)(3y + 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 + x)' equal to zero and attempt to solve:

Simplifying
2y + x = 0

Reorder the terms:
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

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

Simplifying
3y + 2x = 0

Reorder the terms:
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y
Solution
x = {0, -2y, -1.5y}

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