2r^2+8r+12=r^2

Solution for 2r^2+8r+12=r^2 equation:

Simplifying
2r2 + 8r + 12 = r2

Reorder the terms:
12 + 8r + 2r2 = r2

Solving
12 + 8r + 2r2 = r2

Solving for variable 'r'.

Combine like terms: 2r2 + -1r2 = 1r2
12 + 8r + 1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
12 + 8r + 1r2 = 0

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

Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

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

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

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

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

Simplifying
r = -2
Solution
r = {-6, -2}