21r^2=-2-13r

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

Simplifying
21r2 = -2 + -13r

Solving
21r2 = -2 + -13r

Solving for variable 'r'.

Reorder the terms:
2 + 13r + 21r2 = -2 + -13r + 2 + 13r

Reorder the terms:
2 + 13r + 21r2 = -2 + 2 + -13r + 13r

Combine like terms: -2 + 2 = 0
2 + 13r + 21r2 = 0 + -13r + 13r
2 + 13r + 21r2 = -13r + 13r

Combine like terms: -13r + 13r = 0
2 + 13r + 21r2 = 0

Factor a trinomial.
(1 + 3r)(2 + 7r) = 0

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

Simplifying
1 + 3r = 0

Solving
1 + 3r = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3r = 0 + -1

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

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

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
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 = {-0.3333333333, -0.2857142857}