(2*x^2)+4x=0

Solution for (2*x^2)+4x=0 equation:

Simplifying
(2x2) + 4x = 0

Reorder the terms:
4x + (2x2) = 0

Solving
4x + (2x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + x) = 0

Ignore the factor 2.
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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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