10r^2-21r+6=0

Solution for 10r^2-21r+6=0 equation:

Simplifying
10r2 + -21r + 6 = 0

Reorder the terms:
6 + -21r + 10r2 = 0

Solving
6 + -21r + 10r2 = 0

Solving for variable 'r'.

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

Divide each side by '10'.
0.6 + -2.1r + r2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -2.1r + -0.6 + r2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -2.1r + r2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -2.1r + r2 = 0 + -0.6
-2.1r + r2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-2.1r + r2 = -0.6

The r term is -2.1r.  Take half its coefficient (-1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
-2.1r + 1.1025 + r2 = -0.6 + 1.1025

Reorder the terms:
1.1025 + -2.1r + r2 = -0.6 + 1.1025

Combine like terms: -0.6 + 1.1025 = 0.5025
1.1025 + -2.1r + r2 = 0.5025

Factor a perfect square on the left side:
(r + -1.05)(r + -1.05) = 0.5025

Calculate the square root of the right side: 0.708872344

Break this problem into two subproblems by setting 
(r + -1.05) equal to 0.708872344 and -0.708872344.

Subproblem 1
r + -1.05 = 0.708872344

Simplifying
r + -1.05 = 0.708872344

Reorder the terms:
-1.05 + r = 0.708872344

Solving
-1.05 + r = 0.708872344

Solving for variable 'r'.

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

Add '1.05' to each side of the equation.
-1.05 + 1.05 + r = 0.708872344 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + r = 0.708872344 + 1.05
r = 0.708872344 + 1.05

Combine like terms: 0.708872344 + 1.05 = 1.758872344
r = 1.758872344

Simplifying
r = 1.758872344

Subproblem 2
r + -1.05 = -0.708872344

Simplifying
r + -1.05 = -0.708872344

Reorder the terms:
-1.05 + r = -0.708872344

Solving
-1.05 + r = -0.708872344

Solving for variable 'r'.

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

Add '1.05' to each side of the equation.
-1.05 + 1.05 + r = -0.708872344 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + r = -0.708872344 + 1.05
r = -0.708872344 + 1.05

Combine like terms: -0.708872344 + 1.05 = 0.341127656
r = 0.341127656

Simplifying
r = 0.341127656

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.758872344, 0.341127656}