3r^2+8r-82=-2

Solution for 3r^2+8r-82=-2 equation:

Simplifying
3r2 + 8r + -82 = -2

Reorder the terms:
-82 + 8r + 3r2 = -2

Solving
-82 + 8r + 3r2 = -2

Solving for variable 'r'.

Reorder the terms:
-82 + 2 + 8r + 3r2 = -2 + 2

Combine like terms: -82 + 2 = -80
-80 + 8r + 3r2 = -2 + 2

Combine like terms: -2 + 2 = 0
-80 + 8r + 3r2 = 0

Factor a trinomial.
(-20 + -3r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-20 + -3r)' equal to zero and attempt to solve:

Simplifying
-20 + -3r = 0

Solving
-20 + -3r = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3r = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3r = 0 + 20
-3r = 0 + 20

Combine like terms: 0 + 20 = 20
-3r = 20

Divide each side by '-3'.
r = -6.666666667

Simplifying
r = -6.666666667
Subproblem 2
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
Solution
r = {-6.666666667, 4}