r^2=19r-88

Solution for r^2=19r-88 equation:

Simplifying
r2 = 19r + -88

Reorder the terms:
r2 = -88 + 19r

Solving
r2 = -88 + 19r

Solving for variable 'r'.

Reorder the terms:
88 + -19r + r2 = -88 + 19r + 88 + -19r

Reorder the terms:
88 + -19r + r2 = -88 + 88 + 19r + -19r

Combine like terms: -88 + 88 = 0
88 + -19r + r2 = 0 + 19r + -19r
88 + -19r + r2 = 19r + -19r

Combine like terms: 19r + -19r = 0
88 + -19r + r2 = 0

Factor a trinomial.
(8 + -1r)(11 + -1r) = 0

Subproblem 1
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Subproblem 2
Set the factor '(11 + -1r)' equal to zero and attempt to solve:

Simplifying
11 + -1r = 0

Solving
11 + -1r = 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 + -1r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1r = 0 + -11
-1r = 0 + -11

Combine like terms: 0 + -11 = -11
-1r = -11

Divide each side by '-1'.
r = 11

Simplifying
r = 11
Solution
r = {8, 11}