5r^2+12r=4r^2-4

Solution for 5r^2+12r=4r^2-4 equation:

Simplifying
5r2 + 12r = 4r2 + -4

Reorder the terms:
12r + 5r2 = 4r2 + -4

Reorder the terms:
12r + 5r2 = -4 + 4r2

Solving
12r + 5r2 = -4 + 4r2

Solving for variable 'r'.

Reorder the terms:
4 + 12r + 5r2 + -4r2 = -4 + 4r2 + 4 + -4r2

Combine like terms: 5r2 + -4r2 = 1r2
4 + 12r + 1r2 = -4 + 4r2 + 4 + -4r2

Reorder the terms:
4 + 12r + 1r2 = -4 + 4 + 4r2 + -4r2

Combine like terms: -4 + 4 = 0
4 + 12r + 1r2 = 0 + 4r2 + -4r2
4 + 12r + 1r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
4 + 12r + 1r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 12r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + 12r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 12r + r2 = 0 + -4
12r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
12r + r2 = -4

The r term is 12r.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12r + 36 + r2 = -4 + 36

Reorder the terms:
36 + 12r + r2 = -4 + 36

Combine like terms: -4 + 36 = 32
36 + 12r + r2 = 32

Factor a perfect square on the left side:
(r + 6)(r + 6) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(r + 6) equal to 5.656854249 and -5.656854249.

Subproblem 1
r + 6 = 5.656854249

Simplifying
r + 6 = 5.656854249

Reorder the terms:
6 + r = 5.656854249

Solving
6 + r = 5.656854249

Solving for variable 'r'.

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

Add '-6' to each side of the equation.
6 + -6 + r = 5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + r = 5.656854249 + -6
r = 5.656854249 + -6

Combine like terms: 5.656854249 + -6 = -0.343145751
r = -0.343145751

Simplifying
r = -0.343145751

Subproblem 2
r + 6 = -5.656854249

Simplifying
r + 6 = -5.656854249

Reorder the terms:
6 + r = -5.656854249

Solving
6 + r = -5.656854249

Solving for variable 'r'.

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

Add '-6' to each side of the equation.
6 + -6 + r = -5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + r = -5.656854249 + -6
r = -5.656854249 + -6

Combine like terms: -5.656854249 + -6 = -11.656854249
r = -11.656854249

Simplifying
r = -11.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.343145751, -11.656854249}