(x+y)(2x^2+x)=0

Solution for (x+y)(2x^2+x)=0 equation:

Simplifying
(x + y)(2x2 + x) = 0

Reorder the terms:
(x + y)(x + 2x2) = 0

Multiply (x + y) * (x + 2x2)
(x(x + 2x2) + y(x + 2x2)) = 0
((x * x + 2x2 * x) + y(x + 2x2)) = 0
((x2 + 2x3) + y(x + 2x2)) = 0
(x2 + 2x3 + (x * y + 2x2 * y)) = 0
(x2 + 2x3 + (xy + 2x2y)) = 0

Reorder the terms:
(xy + x2 + 2x2y + 2x3) = 0
(xy + x2 + 2x2y + 2x3) = 0

Solving
xy + x2 + 2x2y + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(y + x + 2xy + 2x2) = 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 '(y + x + 2xy + 2x2)' equal to zero and attempt to solve:

Simplifying
y + x + 2xy + 2x2 = 0

Reorder the terms:
x + 2xy + 2x2 + y = 0

Solving
x + 2xy + 2x2 + y = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}