40=r(r-3)

Solution for 40=r(r-3) equation:

Simplifying
40 = r(r + -3)

Reorder the terms:
40 = r(-3 + r)
40 = (-3 * r + r * r)
40 = (-3r + r2)

Solving
40 = -3r + r2

Solving for variable 'r'.

Reorder the terms:
40 + 3r + -1r2 = -3r + 3r + r2 + -1r2

Combine like terms: -3r + 3r = 0
40 + 3r + -1r2 = 0 + r2 + -1r2
40 + 3r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
40 + 3r + -1r2 = 0

Factor a trinomial.
(8 + -1r)(5 + r) = 0

Subproblem 1
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Subproblem 2
Set the factor '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

Solving
5 + r = 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 + r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Solution
r = {8, -5}