(0.5+x+0.5)x=

Solution for (0.5+x+0.5)x= equation:

Simplifying
(0.5 + x + 0.5) * x = 0

Reorder the terms:
(0.5 + 0.5 + x) * x = 0

Combine like terms: 0.5 + 0.5 = 1
(1 + x) * x = 0

Reorder the terms for easier multiplication:
x(1 + x) = 0
(1 * x + x * x) = 0
(1x + x2) = 0

Solving
1x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0, -1}