=x(2x+1)

Solution for =x(2x+1) equation:

Simplifying
0 = x(2x + 1)

Reorder the terms:
0 = x(1 + 2x)
0 = (1 * x + 2x * x)
0 = (1x + 2x2)

Solving
0 = 1x + 2x2

Solving for variable 'x'.
Remove the zero:
-1x + -2x2 = 1x + 2x2 + -1x + -2x2

Reorder the terms:
-1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
-1x + -2x2 = 0 + 2x2 + -2x2
-1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + 2x) = 0

Ignore the factor -1.
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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}