0.25=[0.25*(r+1)-1]

Solution for 0.25=[0.25*(r+1)-1] equation:

Simplifying
0.25 = [0.25(r + 1) + -1]

Reorder the terms:
0.25 = [0.25(1 + r) + -1]
0.25 = [(1 * 0.25 + r * 0.25) + -1]
0.25 = [(0.25 + 0.25r) + -1]

Reorder the terms:
0.25 = [0.25 + -1 + 0.25r]

Combine like terms: 0.25 + -1 = -0.75
0.25 = [-0.75 + 0.25r]

Remove brackets around [-0.75 + 0.25r]
0.25 = -0.75 + 0.25r

Solving
0.25 = -0.75 + 0.25r

Solving for variable 'r'.

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

Add '-0.25r' to each side of the equation.
0.25 + -0.25r = -0.75 + 0.25r + -0.25r

Combine like terms: 0.25r + -0.25r = 0.00
0.25 + -0.25r = -0.75 + 0.00
0.25 + -0.25r = -0.75

Add '-0.25' to each side of the equation.
0.25 + -0.25 + -0.25r = -0.75 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.25r = -0.75 + -0.25
-0.25r = -0.75 + -0.25

Combine like terms: -0.75 + -0.25 = -1
-0.25r = -1

Divide each side by '-0.25'.
r = 4

Simplifying
r = 4