10r^2-21r+-4r=6

Solution for 10r^2-21r+-4r=6 equation:

Simplifying
10r2 + -21r + -4r = 6

Reorder the terms:
-21r + -4r + 10r2 = 6

Combine like terms: -21r + -4r = -25r
-25r + 10r2 = 6

Solving
-25r + 10r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + -25r + 10r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -25r + 10r2 = 0

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

Divide each side by '10'.
-0.6 + -2.5r + r2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.5r + 0.6 + r2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.5r + r2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.5r + r2 = 0 + 0.6
-2.5r + r2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.5r + r2 = 0.6

The r term is -2.5r.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5r + 1.5625 + r2 = 0.6 + 1.5625

Reorder the terms:
1.5625 + -2.5r + r2 = 0.6 + 1.5625

Combine like terms: 0.6 + 1.5625 = 2.1625
1.5625 + -2.5r + r2 = 2.1625

Factor a perfect square on the left side:
(r + -1.25)(r + -1.25) = 2.1625

Calculate the square root of the right side: 1.470544117

Break this problem into two subproblems by setting 
(r + -1.25) equal to 1.470544117 and -1.470544117.

Subproblem 1
r + -1.25 = 1.470544117

Simplifying
r + -1.25 = 1.470544117

Reorder the terms:
-1.25 + r = 1.470544117

Solving
-1.25 + r = 1.470544117

Solving for variable 'r'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + r = 1.470544117 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + r = 1.470544117 + 1.25
r = 1.470544117 + 1.25

Combine like terms: 1.470544117 + 1.25 = 2.720544117
r = 2.720544117

Simplifying
r = 2.720544117

Subproblem 2
r + -1.25 = -1.470544117

Simplifying
r + -1.25 = -1.470544117

Reorder the terms:
-1.25 + r = -1.470544117

Solving
-1.25 + r = -1.470544117

Solving for variable 'r'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + r = -1.470544117 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + r = -1.470544117 + 1.25
r = -1.470544117 + 1.25

Combine like terms: -1.470544117 + 1.25 = -0.220544117
r = -0.220544117

Simplifying
r = -0.220544117

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.720544117, -0.220544117}