8r^2=20+36r

Solution for 8r^2=20+36r equation:

Simplifying
8r2 = 20 + 36r

Solving
8r2 = 20 + 36r

Solving for variable 'r'.

Reorder the terms:
-20 + -36r + 8r2 = 20 + 36r + -20 + -36r

Reorder the terms:
-20 + -36r + 8r2 = 20 + -20 + 36r + -36r

Combine like terms: 20 + -20 = 0
-20 + -36r + 8r2 = 0 + 36r + -36r
-20 + -36r + 8r2 = 36r + -36r

Combine like terms: 36r + -36r = 0
-20 + -36r + 8r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -9r + 2r2) = 0

Factor a trinomial.
4((-1 + -2r)(5 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve:

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-0.5, 5}