(r-2)(r-5)=40

Solution for (r-2)(r-5)=40 equation:

Simplifying
(r + -2)(r + -5) = 40

Reorder the terms:
(-2 + r)(r + -5) = 40

Reorder the terms:
(-2 + r)(-5 + r) = 40

Multiply (-2 + r) * (-5 + r)
(-2(-5 + r) + r(-5 + r)) = 40
((-5 * -2 + r * -2) + r(-5 + r)) = 40
((10 + -2r) + r(-5 + r)) = 40
(10 + -2r + (-5 * r + r * r)) = 40
(10 + -2r + (-5r + r2)) = 40

Combine like terms: -2r + -5r = -7r
(10 + -7r + r2) = 40

Solving
10 + -7r + r2 = 40

Solving for variable 'r'.

Reorder the terms:
10 + -40 + -7r + r2 = 40 + -40

Combine like terms: 10 + -40 = -30
-30 + -7r + r2 = 40 + -40

Combine like terms: 40 + -40 = 0
-30 + -7r + r2 = 0

Factor a trinomial.
(-3 + -1r)(10 + -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 '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-3, 10}