(r+7)(r-5)=5(5-r)

Solution for (r+7)(r-5)=5(5-r) equation:

Simplifying
(r + 7)(r + -5) = 5(5 + -1r)

Reorder the terms:
(7 + r)(r + -5) = 5(5 + -1r)

Reorder the terms:
(7 + r)(-5 + r) = 5(5 + -1r)

Multiply (7 + r) * (-5 + r)
(7(-5 + r) + r(-5 + r)) = 5(5 + -1r)
((-5 * 7 + r * 7) + r(-5 + r)) = 5(5 + -1r)
((-35 + 7r) + r(-5 + r)) = 5(5 + -1r)
(-35 + 7r + (-5 * r + r * r)) = 5(5 + -1r)
(-35 + 7r + (-5r + r2)) = 5(5 + -1r)

Combine like terms: 7r + -5r = 2r
(-35 + 2r + r2) = 5(5 + -1r)
-35 + 2r + r2 = (5 * 5 + -1r * 5)
-35 + 2r + r2 = (25 + -5r)

Solving
-35 + 2r + r2 = 25 + -5r

Solving for variable 'r'.

Reorder the terms:
-35 + -25 + 2r + 5r + r2 = 25 + -5r + -25 + 5r

Combine like terms: -35 + -25 = -60
-60 + 2r + 5r + r2 = 25 + -5r + -25 + 5r

Combine like terms: 2r + 5r = 7r
-60 + 7r + r2 = 25 + -5r + -25 + 5r

Reorder the terms:
-60 + 7r + r2 = 25 + -25 + -5r + 5r

Combine like terms: 25 + -25 = 0
-60 + 7r + r2 = 0 + -5r + 5r
-60 + 7r + r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
-60 + 7r + r2 = 0

Factor a trinomial.
(-12 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-12 + -1r)' equal to zero and attempt to solve:

Simplifying
-12 + -1r = 0

Solving
-12 + -1r = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1r = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1r = 0 + 12
-1r = 0 + 12

Combine like terms: 0 + 12 = 12
-1r = 12

Divide each side by '-1'.
r = -12

Simplifying
r = -12
Subproblem 2
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
Solution
r = {-12, 5}