21r^2+64r-20=0

Solution for 21r^2+64r-20=0 equation:

Simplifying
21r2 + 64r + -20 = 0

Reorder the terms:
-20 + 64r + 21r2 = 0

Solving
-20 + 64r + 21r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-10 + -3r)(2 + -7r) = 0

Subproblem 1
Set the factor '(-10 + -3r)' equal to zero and attempt to solve:

Simplifying
-10 + -3r = 0

Solving
-10 + -3r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3r = 0 + 10
-3r = 0 + 10

Combine like terms: 0 + 10 = 10
-3r = 10

Divide each side by '-3'.
r = -3.333333333

Simplifying
r = -3.333333333
Subproblem 2
Set the factor '(2 + -7r)' equal to zero and attempt to solve:

Simplifying
2 + -7r = 0

Solving
2 + -7r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7r = 0 + -2

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

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

Divide each side by '-7'.
r = 0.2857142857

Simplifying
r = 0.2857142857
Solution
r = {-3.333333333, 0.2857142857}