21r^2+240r+300=0

Solution for 21r^2+240r+300=0 equation:

Simplifying
21r2 + 240r + 300 = 0

Reorder the terms:
300 + 240r + 21r2 = 0

Solving
300 + 240r + 21r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(100 + 80r + 7r2) = 0

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

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

Simplifying
10 + r = 0

Solving
10 + r = 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 + r = 0 + -10

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

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

Simplifying
r = -10
Subproblem 2
Set the factor '(10 + 7r)' equal to zero and attempt to solve:

Simplifying
10 + 7r = 0

Solving
10 + 7r = 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 + 7r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7r = 0 + -10
7r = 0 + -10

Combine like terms: 0 + -10 = -10
7r = -10

Divide each side by '7'.
r = -1.428571429

Simplifying
r = -1.428571429
Solution
r = {-10, -1.428571429}