12r^2-21=3r

Solution for 12r^2-21=3r equation:

Simplifying
12r2 + -21 = 3r

Reorder the terms:
-21 + 12r2 = 3r

Solving
-21 + 12r2 = 3r

Solving for variable 'r'.

Reorder the terms:
-21 + -3r + 12r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
-21 + -3r + 12r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -1r + 4r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1r + 4r2)' equal to zero and attempt to solve:

Simplifying
-7 + -1r + 4r2 = 0

Solving
-7 + -1r + 4r2 = 0

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

Divide each side by '4'.
-1.75 + -0.25r + r2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.25r + 1.75 + r2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.25r + r2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.25r + r2 = 0 + 1.75
-0.25r + r2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.25r + r2 = 1.75

The r term is -0.25r.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25r + 0.015625 + r2 = 1.75 + 0.015625

Reorder the terms:
0.015625 + -0.25r + r2 = 1.75 + 0.015625

Combine like terms: 1.75 + 0.015625 = 1.765625
0.015625 + -0.25r + r2 = 1.765625

Factor a perfect square on the left side:
(r + -0.125)(r + -0.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(r + -0.125) equal to 1.328768227 and -1.328768227.

Subproblem 1
r + -0.125 = 1.328768227

Simplifying
r + -0.125 = 1.328768227

Reorder the terms:
-0.125 + r = 1.328768227

Solving
-0.125 + r = 1.328768227

Solving for variable 'r'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + r = 1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + r = 1.328768227 + 0.125
r = 1.328768227 + 0.125

Combine like terms: 1.328768227 + 0.125 = 1.453768227
r = 1.453768227

Simplifying
r = 1.453768227

Subproblem 2
r + -0.125 = -1.328768227

Simplifying
r + -0.125 = -1.328768227

Reorder the terms:
-0.125 + r = -1.328768227

Solving
-0.125 + r = -1.328768227

Solving for variable 'r'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + r = -1.328768227 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + r = -1.328768227 + 0.125
r = -1.328768227 + 0.125

Combine like terms: -1.328768227 + 0.125 = -1.203768227
r = -1.203768227

Simplifying
r = -1.203768227

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.453768227, -1.203768227}
Solution
r = {1.453768227, -1.203768227}