.20(x)+x=x(x+.20)

Solution for .20(x)+x=x(x+.20) equation:

Simplifying
0.20(x) + x = x(x + 0.20)

Combine like terms: 0.20x + x = 1.2x
1.2x = x(x + 0.20)

Reorder the terms:
1.2x = x(0.20 + x)
1.2x = (0.20 * x + x * x)
1.2x = (0.20x + x2)

Solving
1.2x = 0.20x + x2

Solving for variable 'x'.

Combine like terms: 1.2x + -0.20x = 1x
1x + -1x2 = 0.20x + x2 + -0.20x + -1x2

Reorder the terms:
1x + -1x2 = 0.20x + -0.20x + x2 + -1x2

Combine like terms: 0.20x + -0.20x = 0.00
1x + -1x2 = 0.00 + x2 + -1x2
1x + -1x2 = x2 + -1x2

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

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

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