r^2-r-23=7

Solution for r^2-r-23=7 equation:

Simplifying
r2 + -1r + -23 = 7

Reorder the terms:
-23 + -1r + r2 = 7

Solving
-23 + -1r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-23 + -7 + -1r + r2 = 7 + -7

Combine like terms: -23 + -7 = -30
-30 + -1r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-30 + -1r + r2 = 0

Factor a trinomial.
(-5 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-5, 6}