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

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

Simplifying
10r2 + -2r = -4r + 6

Reorder the terms:
-2r + 10r2 = -4r + 6

Reorder the terms:
-2r + 10r2 = 6 + -4r

Solving
-2r + 10r2 = 6 + -4r

Solving for variable 'r'.

Reorder the terms:
-6 + -2r + 4r + 10r2 = 6 + -4r + -6 + 4r

Combine like terms: -2r + 4r = 2r
-6 + 2r + 10r2 = 6 + -4r + -6 + 4r

Reorder the terms:
-6 + 2r + 10r2 = 6 + -6 + -4r + 4r

Combine like terms: 6 + -6 = 0
-6 + 2r + 10r2 = 0 + -4r + 4r
-6 + 2r + 10r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-6 + 2r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + r + 5r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + r + 5r2)' equal to zero and attempt to solve:

Simplifying
-3 + r + 5r2 = 0

Solving
-3 + r + 5r2 = 0

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

Divide each side by '5'.
-0.6 + 0.2r + r2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.2r + 0.6 + r2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.2r + r2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.2r + r2 = 0 + 0.6
0.2r + r2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.2r + r2 = 0.6

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2r + 0.25 + r2 = 0.6 + 0.25

Reorder the terms:
0.25 + 0.2r + r2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + 0.2r + r2 = 0.85

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
r + 0.5 = 0.921954446

Simplifying
r + 0.5 = 0.921954446

Reorder the terms:
0.5 + r = 0.921954446

Solving
0.5 + r = 0.921954446

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.921954446 + -0.5
r = 0.921954446 + -0.5

Combine like terms: 0.921954446 + -0.5 = 0.421954446
r = 0.421954446

Simplifying
r = 0.421954446

Subproblem 2
r + 0.5 = -0.921954446

Simplifying
r + 0.5 = -0.921954446

Reorder the terms:
0.5 + r = -0.921954446

Solving
0.5 + r = -0.921954446

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -0.921954446 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.921954446 + -0.5
r = -0.921954446 + -0.5

Combine like terms: -0.921954446 + -0.5 = -1.421954446
r = -1.421954446

Simplifying
r = -1.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.421954446, -1.421954446}
Solution
r = {0.421954446, -1.421954446}