40=r(r-6)

Solution for 40=r(r-6) equation:

Simplifying
40 = r(r + -6)

Reorder the terms:
40 = r(-6 + r)
40 = (-6 * r + r * r)
40 = (-6r + r2)

Solving
40 = -6r + r2

Solving for variable 'r'.

Reorder the terms:
40 + 6r + -1r2 = -6r + 6r + r2 + -1r2

Combine like terms: -6r + 6r = 0
40 + 6r + -1r2 = 0 + r2 + -1r2
40 + 6r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
40 + 6r + -1r2 = 0

Factor a trinomial.
(10 + -1r)(4 + r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Solution
r = {10, -4}