10r^2+10r+6=12r

Solution for 10r^2+10r+6=12r equation:

Simplifying
10r2 + 10r + 6 = 12r

Reorder the terms:
6 + 10r + 10r2 = 12r

Solving
6 + 10r + 10r2 = 12r

Solving for variable 'r'.

Reorder the terms:
6 + 10r + -12r + 10r2 = 12r + -12r

Combine like terms: 10r + -12r = -2r
6 + -2r + 10r2 = 12r + -12r

Combine like terms: 12r + -12r = 0
6 + -2r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1r + 5r2) = 0

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

Simplifying
3 + -1r + 5r2 = 0

Solving
3 + -1r + 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 -0.2r.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2r + 0.01 + r2 = -0.6 + 0.01

Reorder the terms:
0.01 + -0.2r + r2 = -0.6 + 0.01

Combine like terms: -0.6 + 0.01 = -0.59
0.01 + -0.2r + r2 = -0.59

Factor a perfect square on the left side:
(r + -0.1)(r + -0.1) = -0.59

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.