Simplifying
4 + x + -1(1.25(2.02 + x)) = 0.1
4 + x + -1((2.02 * 1.25 + x * 1.25)) = 0.1
4 + x + -1((2.525 + 1.25x)) = 0.1
4 + x + (2.525 * -1 + 1.25x * -1) = 0.1
4 + x + (-2.525 + -1.25x) = 0.1

Reorder the terms:
4 + -2.525 + x + -1.25x = 0.1

Combine like terms: 4 + -2.525 = 1.475
1.475 + x + -1.25x = 0.1

Combine like terms: x + -1.25x = -0.25x
1.475 + -0.25x = 0.1

Solving
1.475 + -0.25x = 0.1

Solving for variable 'x'.

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

Add '-1.475' to each side of the equation.
1.475 + -1.475 + -0.25x = 0.1 + -1.475

Combine like terms: 1.475 + -1.475 = 0.000
0.000 + -0.25x = 0.1 + -1.475
-0.25x = 0.1 + -1.475

Combine like terms: 0.1 + -1.475 = -1.375
-0.25x = -1.375

Divide each side by '-0.25'.
x = 5.5

Simplifying
x = 5.5