-2r^2+28r-96=0

Solution for -2r^2+28r-96=0 equation:

Simplifying
-2r2 + 28r + -96 = 0

Reorder the terms:
-96 + 28r + -2r2 = 0

Solving
-96 + 28r + -2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 14r + -1r2) = 0

Factor a trinomial.
2((-8 + r)(6 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + r)' equal to zero and attempt to solve:

Simplifying
-8 + r = 0

Solving
-8 + r = 0

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

Add '8' to each side of the equation.
-8 + 8 + r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + r = 0 + 8
r = 0 + 8

Combine like terms: 0 + 8 = 8
r = 8

Simplifying
r = 8
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 = {8, 6}