(r+9)(r-6)=4(6-r)

Solution for (r+9)(r-6)=4(6-r) equation:

Simplifying
(r + 9)(r + -6) = 4(6 + -1r)

Reorder the terms:
(9 + r)(r + -6) = 4(6 + -1r)

Reorder the terms:
(9 + r)(-6 + r) = 4(6 + -1r)

Multiply (9 + r) * (-6 + r)
(9(-6 + r) + r(-6 + r)) = 4(6 + -1r)
((-6 * 9 + r * 9) + r(-6 + r)) = 4(6 + -1r)
((-54 + 9r) + r(-6 + r)) = 4(6 + -1r)
(-54 + 9r + (-6 * r + r * r)) = 4(6 + -1r)
(-54 + 9r + (-6r + r2)) = 4(6 + -1r)

Combine like terms: 9r + -6r = 3r
(-54 + 3r + r2) = 4(6 + -1r)
-54 + 3r + r2 = (6 * 4 + -1r * 4)
-54 + 3r + r2 = (24 + -4r)

Solving
-54 + 3r + r2 = 24 + -4r

Solving for variable 'r'.

Reorder the terms:
-54 + -24 + 3r + 4r + r2 = 24 + -4r + -24 + 4r

Combine like terms: -54 + -24 = -78
-78 + 3r + 4r + r2 = 24 + -4r + -24 + 4r

Combine like terms: 3r + 4r = 7r
-78 + 7r + r2 = 24 + -4r + -24 + 4r

Reorder the terms:
-78 + 7r + r2 = 24 + -24 + -4r + 4r

Combine like terms: 24 + -24 = 0
-78 + 7r + r2 = 0 + -4r + 4r
-78 + 7r + r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-78 + 7r + r2 = 0

Factor a trinomial.
(-13 + -1r)(6 + -1r) = 0

Subproblem 1
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
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 = {-13, 6}