2r^2=6r+36

Solution for 2r^2=6r+36 equation:

Simplifying
2r2 = 6r + 36

Reorder the terms:
2r2 = 36 + 6r

Solving
2r2 = 36 + 6r

Solving for variable 'r'.

Reorder the terms:
-36 + -6r + 2r2 = 36 + 6r + -36 + -6r

Reorder the terms:
-36 + -6r + 2r2 = 36 + -36 + 6r + -6r

Combine like terms: 36 + -36 = 0
-36 + -6r + 2r2 = 0 + 6r + -6r
-36 + -6r + 2r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
-36 + -6r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3r + r2) = 0

Factor a trinomial.
2((-3 + -1r)(6 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-3, 6}