6r^2-12r=288

Solution for 6r^2-12r=288 equation:

Simplifying
6r2 + -12r = 288

Reorder the terms:
-12r + 6r2 = 288

Solving
-12r + 6r2 = 288

Solving for variable 'r'.

Reorder the terms:
-288 + -12r + 6r2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + -12r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-48 + -2r + r2) = 0

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

Ignore the factor 6.
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}