r^2+12r+6+r+6r^2=0

Solution for r^2+12r+6+r+6r^2=0 equation:

Simplifying
r2 + 12r + 6 + r + 6r2 = 0

Reorder the terms:
6 + 12r + r + r2 + 6r2 = 0

Combine like terms: 12r + r = 13r
6 + 13r + r2 + 6r2 = 0

Combine like terms: r2 + 6r2 = 7r2
6 + 13r + 7r2 = 0

Solving
6 + 13r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + r)(6 + 7r) = 0

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

Simplifying
1 + r = 0

Solving
1 + r = 0

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

Add '-1' to each side of the equation.
1 + -1 + r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0 + -1
r = 0 + -1

Combine like terms: 0 + -1 = -1
r = -1

Simplifying
r = -1
Subproblem 2
Set the factor '(6 + 7r)' equal to zero and attempt to solve:

Simplifying
6 + 7r = 0

Solving
6 + 7r = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7r = 0 + -6
7r = 0 + -6

Combine like terms: 0 + -6 = -6
7r = -6

Divide each side by '7'.
r = -0.8571428571

Simplifying
r = -0.8571428571
Solution
r = {-1, -0.8571428571}