3r^2-12r-3=6-2r^2

Solution for 3r^2-12r-3=6-2r^2 equation:

Simplifying
3r2 + -12r + -3 = 6 + -2r2

Reorder the terms:
-3 + -12r + 3r2 = 6 + -2r2

Solving
-3 + -12r + 3r2 = 6 + -2r2

Solving for variable 'r'.

Reorder the terms:
-3 + -6 + -12r + 3r2 + 2r2 = 6 + -2r2 + -6 + 2r2

Combine like terms: -3 + -6 = -9
-9 + -12r + 3r2 + 2r2 = 6 + -2r2 + -6 + 2r2

Combine like terms: 3r2 + 2r2 = 5r2
-9 + -12r + 5r2 = 6 + -2r2 + -6 + 2r2

Reorder the terms:
-9 + -12r + 5r2 = 6 + -6 + -2r2 + 2r2

Combine like terms: 6 + -6 = 0
-9 + -12r + 5r2 = 0 + -2r2 + 2r2
-9 + -12r + 5r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
-9 + -12r + 5r2 = 0

Factor a trinomial.
(-3 + -5r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -5r)' equal to zero and attempt to solve:

Simplifying
-3 + -5r = 0

Solving
-3 + -5r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5r = 0 + 3
-5r = 0 + 3

Combine like terms: 0 + 3 = 3
-5r = 3

Divide each side by '-5'.
r = -0.6

Simplifying
r = -0.6
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.6, 3}