r^2-12r-37=8

Solution for r^2-12r-37=8 equation:

Simplifying
r2 + -12r + -37 = 8

Reorder the terms:
-37 + -12r + r2 = 8

Solving
-37 + -12r + r2 = 8

Solving for variable 'r'.

Reorder the terms:
-37 + -8 + -12r + r2 = 8 + -8

Combine like terms: -37 + -8 = -45
-45 + -12r + r2 = 8 + -8

Combine like terms: 8 + -8 = 0
-45 + -12r + r2 = 0

Factor a trinomial.
(-3 + -1r)(15 + -1r) = 0

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

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(15 + -1r)' equal to zero and attempt to solve:

Simplifying
15 + -1r = 0

Solving
15 + -1r = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1r = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1r = 0 + -15
-1r = 0 + -15

Combine like terms: 0 + -15 = -15
-1r = -15

Divide each side by '-1'.
r = 15

Simplifying
r = 15
Solution
r = {-3, 15}