r^2-12r-6=7

Solution for r^2-12r-6=7 equation:

Simplifying
r2 + -12r + -6 = 7

Reorder the terms:
-6 + -12r + r2 = 7

Solving
-6 + -12r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-6 + -7 + -12r + r2 = 7 + -7

Combine like terms: -6 + -7 = -13
-13 + -12r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-13 + -12r + r2 = 0

Factor a trinomial.
(-1 + -1r)(13 + -1r) = 0

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(13 + -1r)' equal to zero and attempt to solve:

Simplifying
13 + -1r = 0

Solving
13 + -1r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1r = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1r = 0 + -13
-1r = 0 + -13

Combine like terms: 0 + -13 = -13
-1r = -13

Divide each side by '-1'.
r = 13

Simplifying
r = 13
Solution
r = {-1, 13}