3r^2-13r=-4

Solution for 3r^2-13r=-4 equation:

Simplifying
3r2 + -13r = -4

Reorder the terms:
-13r + 3r2 = -4

Solving
-13r + 3r2 = -4

Solving for variable 'r'.

Reorder the terms:
4 + -13r + 3r2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -13r + 3r2 = 0

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

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {0.3333333333, 4}