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 = 9r2
4 + 12r + 9r2 = -4 + -4r2 + 4 + 4r2

Reorder the terms:
4 + 12r + 9r2 = -4 + 4 + -4r2 + 4r2

Combine like terms: -4 + 4 = 0
4 + 12r + 9r2 = 0 + -4r2 + 4r2
4 + 12r + 9r2 = -4r2 + 4r2

Combine like terms: -4r2 + 4r2 = 0
4 + 12r + 9r2 = 0

Factor a trinomial.
(2 + 3r)(2 + 3r) = 0

Subproblem 1
Set the factor '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Subproblem 2
Set the factor '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Solution
r = {-0.6666666667, -0.6666666667}