6r^2-144=6r+3r^2

Solution for 6r^2-144=6r+3r^2 equation:

Simplifying
6r2 + -144 = 6r + 3r2

Reorder the terms:
-144 + 6r2 = 6r + 3r2

Solving
-144 + 6r2 = 6r + 3r2

Solving for variable 'r'.

Reorder the terms:
-144 + -6r + 6r2 + -3r2 = 6r + 3r2 + -6r + -3r2

Combine like terms: 6r2 + -3r2 = 3r2
-144 + -6r + 3r2 = 6r + 3r2 + -6r + -3r2

Reorder the terms:
-144 + -6r + 3r2 = 6r + -6r + 3r2 + -3r2

Combine like terms: 6r + -6r = 0
-144 + -6r + 3r2 = 0 + 3r2 + -3r2
-144 + -6r + 3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
-144 + -6r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-48 + -2r + r2) = 0

Factor a trinomial.
3((-6 + -1r)(8 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 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 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

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

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

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-6, 8}