166r=-8r-180-24r^2

Solution for 166r=-8r-180-24r^2 equation:

Simplifying
166r = -8r + -180 + -24r2

Reorder the terms:
166r = -180 + -8r + -24r2

Solving
166r = -180 + -8r + -24r2

Solving for variable 'r'.

Reorder the terms:
180 + 166r + 8r + 24r2 = -180 + -8r + -24r2 + 180 + 8r + 24r2

Combine like terms: 166r + 8r = 174r
180 + 174r + 24r2 = -180 + -8r + -24r2 + 180 + 8r + 24r2

Reorder the terms:
180 + 174r + 24r2 = -180 + 180 + -8r + 8r + -24r2 + 24r2

Combine like terms: -180 + 180 = 0
180 + 174r + 24r2 = 0 + -8r + 8r + -24r2 + 24r2
180 + 174r + 24r2 = -8r + 8r + -24r2 + 24r2

Combine like terms: -8r + 8r = 0
180 + 174r + 24r2 = 0 + -24r2 + 24r2
180 + 174r + 24r2 = -24r2 + 24r2

Combine like terms: -24r2 + 24r2 = 0
180 + 174r + 24r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + 29r + 4r2) = 0

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

Ignore the factor 6.
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 '(5 + 4r)' equal to zero and attempt to solve:

Simplifying
5 + 4r = 0

Solving
5 + 4r = 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 + 4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4r = 0 + -5
4r = 0 + -5

Combine like terms: 0 + -5 = -5
4r = -5

Divide each side by '4'.
r = -1.25

Simplifying
r = -1.25
Solution
r = {-6, -1.25}