3r^2+r=30

Solution for 3r^2+r=30 equation:

Simplifying
3r2 + r = 30

Reorder the terms:
r + 3r2 = 30

Solving
r + 3r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + r + 3r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + r + 3r2 = 0

Factor a trinomial.
(-10 + -3r)(3 + -1r) = 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 '(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
Solution
r = {-3.333333333, 3}