5r^2-19r-4=0

Solution for 5r^2-19r-4=0 equation:

Simplifying
5r2 + -19r + -4 = 0

Reorder the terms:
-4 + -19r + 5r2 = 0

Solving
-4 + -19r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -5r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-1 + -5r)' equal to zero and attempt to solve:

Simplifying
-1 + -5r = 0

Solving
-1 + -5r = 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 + -5r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5r = 0 + 1
-5r = 0 + 1

Combine like terms: 0 + 1 = 1
-5r = 1

Divide each side by '-5'.
r = -0.2

Simplifying
r = -0.2
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 = {-0.2, 4}