-8r^2-2r+21=0

Solution for -8r^2-2r+21=0 equation:

Simplifying
-8r2 + -2r + 21 = 0

Reorder the terms:
21 + -2r + -8r2 = 0

Solving
21 + -2r + -8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -2r)(7 + 4r) = 0

Subproblem 1
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Subproblem 2
Set the factor '(7 + 4r)' equal to zero and attempt to solve:

Simplifying
7 + 4r = 0

Solving
7 + 4r = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4r = 0 + -7
4r = 0 + -7

Combine like terms: 0 + -7 = -7
4r = -7

Divide each side by '4'.
r = -1.75

Simplifying
r = -1.75
Solution
r = {1.5, -1.75}