r^2-4r-15=-3

Solution for r^2-4r-15=-3 equation:

Simplifying
r2 + -4r + -15 = -3

Reorder the terms:
-15 + -4r + r2 = -3

Solving
-15 + -4r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
-15 + 3 + -4r + r2 = -3 + 3

Combine like terms: -15 + 3 = -12
-12 + -4r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
-12 + -4r + r2 = 0

Factor a trinomial.
(-2 + -1r)(6 + -1r) = 0

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
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 = {-2, 6}