(.5r+.5)(r+.6)=

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Solution for (.5r+.5)(r+.6)= equation: 


Simplifying
(0.5r + 0.5)(r + 0.6) = 0

Reorder the terms:
(0.5 + 0.5r)(r + 0.6) = 0

Reorder the terms:
(0.5 + 0.5r)(0.6 + r) = 0

Multiply (0.5 + 0.5r) * (0.6 + r)
(0.5(0.6 + r) + 0.5r * (0.6 + r)) = 0
((0.6 * 0.5 + r * 0.5) + 0.5r * (0.6 + r)) = 0
((0.3 + 0.5r) + 0.5r * (0.6 + r)) = 0
(0.3 + 0.5r + (0.6 * 0.5r + r * 0.5r)) = 0
(0.3 + 0.5r + (0.3r + 0.5r2)) = 0

Combine like terms: 0.5r + 0.3r = 0.8r
(0.3 + 0.8r + 0.5r2) = 0

Solving
0.3 + 0.8r + 0.5r2 = 0

Solving for variable 'r'.

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

Divide each side by '0.5'.
0.6 + 1.6r + r2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 1.6r + -0.6 + r2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 1.6r + r2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 1.6r + r2 = 0 + -0.6
1.6r + r2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
1.6r + r2 = -0.6

The r term is 1.6r.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6r + 0.64 + r2 = -0.6 + 0.64

Reorder the terms:
0.64 + 1.6r + r2 = -0.6 + 0.64

Combine like terms: -0.6 + 0.64 = 0.04
0.64 + 1.6r + r2 = 0.04

Factor a perfect square on the left side:
(r + 0.8)(r + 0.8) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(r + 0.8) equal to 0.2 and -0.2.


Subproblem 1
r + 0.8 = 0.2

Simplifying
r + 0.8 = 0.2

Reorder the terms:
0.8 + r = 0.2

Solving
0.8 + r = 0.2

Solving for variable 'r'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + r = 0.2 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + r = 0.2 + -0.8
r = 0.2 + -0.8

Combine like terms: 0.2 + -0.8 = -0.6
r = -0.6

Simplifying
r = -0.6


Subproblem 2
r + 0.8 = -0.2

Simplifying
r + 0.8 = -0.2

Reorder the terms:
0.8 + r = -0.2

Solving
0.8 + r = -0.2

Solving for variable 'r'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + r = -0.2 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + r = -0.2 + -0.8
r = -0.2 + -0.8

Combine like terms: -0.2 + -0.8 = -1
r = -1

Simplifying
r = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.6, -1}

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