8r^2+22r-21=0

Solution for 8r^2+22r-21=0 equation:

Simplifying
8r2 + 22r + -21 = 0

Reorder the terms:
-21 + 22r + 8r2 = 0

Solving
-21 + 22r + 8r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-7 + -2r)' equal to zero and attempt to solve:

Simplifying
-7 + -2r = 0

Solving
-7 + -2r = 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 + -2r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2r = 0 + 7
-2r = 0 + 7

Combine like terms: 0 + 7 = 7
-2r = 7

Divide each side by '-2'.
r = -3.5

Simplifying
r = -3.5
Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 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 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Solution
r = {-3.5, 0.75}