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

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

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

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

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

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

Solving for variable 'r'.

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

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

Reorder the terms:
6 + -25r + 10r2 = -6 + 6 + 4r + -4r

Combine like terms: -6 + 6 = 0
6 + -25r + 10r2 = 0 + 4r + -4r
6 + -25r + 10r2 = 4r + -4r

Combine like terms: 4r + -4r = 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 = 0.9625
1.5625 + -2.5r + r2 = 0.9625

Factor a perfect square on the left side:
(r + -1.25)(r + -1.25) = 0.9625

Calculate the square root of the right side: 0.981070844

Break this problem into two subproblems by setting 
(r + -1.25) equal to 0.981070844 and -0.981070844.

Subproblem 1
r + -1.25 = 0.981070844

Simplifying
r + -1.25 = 0.981070844

Reorder the terms:
-1.25 + r = 0.981070844

Solving
-1.25 + r = 0.981070844

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 = 0.981070844 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + r = 0.981070844 + 1.25
r = 0.981070844 + 1.25

Combine like terms: 0.981070844 + 1.25 = 2.231070844
r = 2.231070844

Simplifying
r = 2.231070844

Subproblem 2
r + -1.25 = -0.981070844

Simplifying
r + -1.25 = -0.981070844

Reorder the terms:
-1.25 + r = -0.981070844

Solving
-1.25 + r = -0.981070844

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 = -0.981070844 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + r = -0.981070844 + 1.25
r = -0.981070844 + 1.25

Combine like terms: -0.981070844 + 1.25 = 0.268929156
r = 0.268929156

Simplifying
r = 0.268929156

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.231070844, 0.268929156}