2r^2=120+8r

Solution for 2r^2=120+8r equation:

Simplifying
2r2 = 120 + 8r

Solving
2r2 = 120 + 8r

Solving for variable 'r'.

Reorder the terms:
-120 + -8r + 2r2 = 120 + 8r + -120 + -8r

Reorder the terms:
-120 + -8r + 2r2 = 120 + -120 + 8r + -8r

Combine like terms: 120 + -120 = 0
-120 + -8r + 2r2 = 0 + 8r + -8r
-120 + -8r + 2r2 = 8r + -8r

Combine like terms: 8r + -8r = 0
-120 + -8r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -4r + r2) = 0

Factor a trinomial.
2((-6 + -1r)(10 + -1r)) = 0

Ignore the factor 2.
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 '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-6, 10}