x(x+2y)=

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

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

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

Solving
2xy + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(2y + x) = 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
Solution
x = {0, -2y}