8r^2+192=-80r

Solution for 8r^2+192=-80r equation:

Simplifying
8r2 + 192 = -80r

Reorder the terms:
192 + 8r2 = -80r

Solving
192 + 8r2 = -80r

Solving for variable 'r'.

Reorder the terms:
192 + 80r + 8r2 = -80r + 80r

Combine like terms: -80r + 80r = 0
192 + 80r + 8r2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(24 + 10r + r2) = 0

Factor a trinomial.
8((6 + r)(4 + r)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 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 + r = 0 + -4

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

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

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