-91=(3r+19)(r-5)

Solution for -91=(3r+19)(r-5) equation:

Simplifying
-91 = (3r + 19)(r + -5)

Reorder the terms:
-91 = (19 + 3r)(r + -5)

Reorder the terms:
-91 = (19 + 3r)(-5 + r)

Multiply (19 + 3r) * (-5 + r)
-91 = (19(-5 + r) + 3r * (-5 + r))
-91 = ((-5 * 19 + r * 19) + 3r * (-5 + r))
-91 = ((-95 + 19r) + 3r * (-5 + r))
-91 = (-95 + 19r + (-5 * 3r + r * 3r))
-91 = (-95 + 19r + (-15r + 3r2))

Combine like terms: 19r + -15r = 4r
-91 = (-95 + 4r + 3r2)

Solving
-91 = -95 + 4r + 3r2

Solving for variable 'r'.

Combine like terms: -91 + 95 = 4
4 + -4r + -3r2 = -95 + 4r + 3r2 + 95 + -4r + -3r2

Reorder the terms:
4 + -4r + -3r2 = -95 + 95 + 4r + -4r + 3r2 + -3r2

Combine like terms: -95 + 95 = 0
4 + -4r + -3r2 = 0 + 4r + -4r + 3r2 + -3r2
4 + -4r + -3r2 = 4r + -4r + 3r2 + -3r2

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

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

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

Subproblem 1
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3r = 0 + -2
-3r = 0 + -2

Combine like terms: 0 + -2 = -2
-3r = -2

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

Simplifying
r = -2
Solution
r = {0.6666666667, -2}