3r^2+7r+13=11

Solution for 3r^2+7r+13=11 equation:

Simplifying
3r2 + 7r + 13 = 11

Reorder the terms:
13 + 7r + 3r2 = 11

Solving
13 + 7r + 3r2 = 11

Solving for variable 'r'.

Reorder the terms:
13 + -11 + 7r + 3r2 = 11 + -11

Combine like terms: 13 + -11 = 2
2 + 7r + 3r2 = 11 + -11

Combine like terms: 11 + -11 = 0
2 + 7r + 3r2 = 0

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

Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

Simplifying
r = -2
Subproblem 2
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
Solution
r = {-2, -0.3333333333}