6r^2+19r-36=0

Solution for 6r^2+19r-36=0 equation:

Simplifying
6r2 + 19r + -36 = 0

Reorder the terms:
-36 + 19r + 6r2 = 0

Solving
-36 + 19r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-9 + -2r)(4 + -3r) = 0

Subproblem 1
Set the factor '(-9 + -2r)' equal to zero and attempt to solve:

Simplifying
-9 + -2r = 0

Solving
-9 + -2r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2r = 0 + 9
-2r = 0 + 9

Combine like terms: 0 + 9 = 9
-2r = 9

Divide each side by '-2'.
r = -4.5

Simplifying
r = -4.5
Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve:

Simplifying
4 + -3r = 0

Solving
4 + -3r = 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 + -3r = 0 + -4

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

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

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Solution
r = {-4.5, 1.333333333}