(r-7)(r+5)=-20

Solution for (r-7)(r+5)=-20 equation:

Simplifying
(r + -7)(r + 5) = -20

Reorder the terms:
(-7 + r)(r + 5) = -20

Reorder the terms:
(-7 + r)(5 + r) = -20

Multiply (-7 + r) * (5 + r)
(-7(5 + r) + r(5 + r)) = -20
((5 * -7 + r * -7) + r(5 + r)) = -20
((-35 + -7r) + r(5 + r)) = -20
(-35 + -7r + (5 * r + r * r)) = -20
(-35 + -7r + (5r + r2)) = -20

Combine like terms: -7r + 5r = -2r
(-35 + -2r + r2) = -20

Solving
-35 + -2r + r2 = -20

Solving for variable 'r'.

Reorder the terms:
-35 + 20 + -2r + r2 = -20 + 20

Combine like terms: -35 + 20 = -15
-15 + -2r + r2 = -20 + 20

Combine like terms: -20 + 20 = 0
-15 + -2r + r2 = 0

Factor a trinomial.
(-3 + -1r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
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 = {-3, 5}