r^2+12r-189=0

Solution for r^2+12r-189=0 equation:

Simplifying
r2 + 12r + -189 = 0

Reorder the terms:
-189 + 12r + r2 = 0

Solving
-189 + 12r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-21 + -1r)(9 + -1r) = 0

Subproblem 1
Set the factor '(-21 + -1r)' equal to zero and attempt to solve:

Simplifying
-21 + -1r = 0

Solving
-21 + -1r = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1r = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1r = 0 + 21
-1r = 0 + 21

Combine like terms: 0 + 21 = 21
-1r = 21

Divide each side by '-1'.
r = -21

Simplifying
r = -21
Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve:

Simplifying
9 + -1r = 0

Solving
9 + -1r = 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 + -1r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1r = 0 + -9
-1r = 0 + -9

Combine like terms: 0 + -9 = -9
-1r = -9

Divide each side by '-1'.
r = 9

Simplifying
r = 9
Solution
r = {-21, 9}