5r^2-120=10r

Solution for 5r^2-120=10r equation:

Simplifying
5r2 + -120 = 10r

Reorder the terms:
-120 + 5r2 = 10r

Solving
-120 + 5r2 = 10r

Solving for variable 'r'.

Reorder the terms:
-120 + -10r + 5r2 = 10r + -10r

Combine like terms: 10r + -10r = 0
-120 + -10r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + -2r + r2) = 0

Factor a trinomial.
5((-4 + -1r)(6 + -1r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
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 = {-4, 6}