3r^2+2r-21=0

Solution for 3r^2+2r-21=0 equation:

Simplifying
3r2 + 2r + -21 = 0

Reorder the terms:
-21 + 2r + 3r2 = 0

Solving
-21 + 2r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -1r)(7 + -3r) = 0

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve:

Simplifying
7 + -3r = 0

Solving
7 + -3r = 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 + -3r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3r = 0 + -7
-3r = 0 + -7

Combine like terms: 0 + -7 = -7
-3r = -7

Divide each side by '-3'.
r = 2.333333333

Simplifying
r = 2.333333333
Solution
r = {-3, 2.333333333}