21r^2-13r-20=0

Solution for 21r^2-13r-20=0 equation:

Simplifying
21r2 + -13r + -20 = 0

Reorder the terms:
-20 + -13r + 21r2 = 0

Solving
-20 + -13r + 21r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -7r)(4 + -3r) = 0

Subproblem 1
Set the factor '(-5 + -7r)' equal to zero and attempt to solve:

Simplifying
-5 + -7r = 0

Solving
-5 + -7r = 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 + -7r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7r = 0 + 5
-7r = 0 + 5

Combine like terms: 0 + 5 = 5
-7r = 5

Divide each side by '-7'.
r = -0.7142857143

Simplifying
r = -0.7142857143
Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve:

Simplifying
4 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Solution
r = {-0.7142857143, 1.333333333}