12r^2+18r=1

Solution for 12r^2+18r=1 equation:

Simplifying
12r2 + 18r = 1

Reorder the terms:
18r + 12r2 = 1

Solving
18r + 12r2 = 1

Solving for variable 'r'.

Reorder the terms:
-1 + 18r + 12r2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 18r + 12r2 = 0

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

Divide each side by '12'.
-0.08333333333 + 1.5r + r2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 1.5r + 0.08333333333 + r2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 1.5r + r2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 1.5r + r2 = 0 + 0.08333333333
1.5r + r2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
1.5r + r2 = 0.08333333333

The r term is 1.5r.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5r + 0.5625 + r2 = 0.08333333333 + 0.5625

Reorder the terms:
0.5625 + 1.5r + r2 = 0.08333333333 + 0.5625

Combine like terms: 0.08333333333 + 0.5625 = 0.64583333333
0.5625 + 1.5r + r2 = 0.64583333333

Factor a perfect square on the left side:
(r + 0.75)(r + 0.75) = 0.64583333333

Calculate the square root of the right side: 0.803637563

Break this problem into two subproblems by setting 
(r + 0.75) equal to 0.803637563 and -0.803637563.

Subproblem 1
r + 0.75 = 0.803637563

Simplifying
r + 0.75 = 0.803637563

Reorder the terms:
0.75 + r = 0.803637563

Solving
0.75 + r = 0.803637563

Solving for variable 'r'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + r = 0.803637563 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + r = 0.803637563 + -0.75
r = 0.803637563 + -0.75

Combine like terms: 0.803637563 + -0.75 = 0.053637563
r = 0.053637563

Simplifying
r = 0.053637563

Subproblem 2
r + 0.75 = -0.803637563

Simplifying
r + 0.75 = -0.803637563

Reorder the terms:
0.75 + r = -0.803637563

Solving
0.75 + r = -0.803637563

Solving for variable 'r'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + r = -0.803637563 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + r = -0.803637563 + -0.75
r = -0.803637563 + -0.75

Combine like terms: -0.803637563 + -0.75 = -1.553637563
r = -1.553637563

Simplifying
r = -1.553637563

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.053637563, -1.553637563}