(0.6r-0.48)(0.05r+1)=0

Solution for (0.6r-0.48)(0.05r+1)=0 equation:

Simplifying
(0.6r + -0.48)(0.05r + 1) = 0

Reorder the terms:
(-0.48 + 0.6r)(0.05r + 1) = 0

Reorder the terms:
(-0.48 + 0.6r)(1 + 0.05r) = 0

Multiply (-0.48 + 0.6r) * (1 + 0.05r)
(-0.48(1 + 0.05r) + 0.6r * (1 + 0.05r)) = 0
((1 * -0.48 + 0.05r * -0.48) + 0.6r * (1 + 0.05r)) = 0
((-0.48 + -0.024r) + 0.6r * (1 + 0.05r)) = 0
(-0.48 + -0.024r + (1 * 0.6r + 0.05r * 0.6r)) = 0
(-0.48 + -0.024r + (0.6r + 0.03r2)) = 0

Combine like terms: -0.024r + 0.6r = 0.576r
(-0.48 + 0.576r + 0.03r2) = 0

Solving
-0.48 + 0.576r + 0.03r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
0.03 the coefficient of the squared term: 

Divide each side by '0.03'.
-16 + 19.2r + r2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 19.2r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + 19.2r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 19.2r + r2 = 0 + 16
19.2r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
19.2r + r2 = 16

The r term is 19.2r.  Take half its coefficient (9.6).
Square it (92.16) and add it to both sides.

Add '92.16' to each side of the equation.
19.2r + 92.16 + r2 = 16 + 92.16

Reorder the terms:
92.16 + 19.2r + r2 = 16 + 92.16

Combine like terms: 16 + 92.16 = 108.16
92.16 + 19.2r + r2 = 108.16

Factor a perfect square on the left side:
(r + 9.6)(r + 9.6) = 108.16

Calculate the square root of the right side: 10.4

Break this problem into two subproblems by setting 
(r + 9.6) equal to 10.4 and -10.4.

Subproblem 1
r + 9.6 = 10.4

Simplifying
r + 9.6 = 10.4

Reorder the terms:
9.6 + r = 10.4

Solving
9.6 + r = 10.4

Solving for variable 'r'.

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

Add '-9.6' to each side of the equation.
9.6 + -9.6 + r = 10.4 + -9.6

Combine like terms: 9.6 + -9.6 = 0.0
0.0 + r = 10.4 + -9.6
r = 10.4 + -9.6

Combine like terms: 10.4 + -9.6 = 0.8
r = 0.8

Simplifying
r = 0.8

Subproblem 2
r + 9.6 = -10.4

Simplifying
r + 9.6 = -10.4

Reorder the terms:
9.6 + r = -10.4

Solving
9.6 + r = -10.4

Solving for variable 'r'.

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

Add '-9.6' to each side of the equation.
9.6 + -9.6 + r = -10.4 + -9.6

Combine like terms: 9.6 + -9.6 = 0.0
0.0 + r = -10.4 + -9.6
r = -10.4 + -9.6

Combine like terms: -10.4 + -9.6 = -20
r = -20

Simplifying
r = -20

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.8, -20}