4r^2+r=33

Solution for 4r^2+r=33 equation:

Simplifying
4r2 + r = 33

Reorder the terms:
r + 4r2 = 33

Solving
r + 4r2 = 33

Solving for variable 'r'.

Reorder the terms:
-33 + r + 4r2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + r + 4r2 = 0

Factor a trinomial.
(-3 + -1r)(11 + -4r) = 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 '(11 + -4r)' equal to zero and attempt to solve:

Simplifying
11 + -4r = 0

Solving
11 + -4r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4r = 0 + -11
-4r = 0 + -11

Combine like terms: 0 + -11 = -11
-4r = -11

Divide each side by '-4'.
r = 2.75

Simplifying
r = 2.75
Solution
r = {-3, 2.75}