14=r(r-5)

Solution for 14=r(r-5) equation:

Simplifying
14 = r(r + -5)

Reorder the terms:
14 = r(-5 + r)
14 = (-5 * r + r * r)
14 = (-5r + r2)

Solving
14 = -5r + r2

Solving for variable 'r'.

Reorder the terms:
14 + 5r + -1r2 = -5r + 5r + r2 + -1r2

Combine like terms: -5r + 5r = 0
14 + 5r + -1r2 = 0 + r2 + -1r2
14 + 5r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
14 + 5r + -1r2 = 0

Factor a trinomial.
(7 + -1r)(2 + r) = 0

Subproblem 1
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

Simplifying
r = -2
Solution
r = {7, -2}