r(r-5)=14

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

Simplifying
r(r + -5) = 14

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

Solving
-5r + r2 = 14

Solving for variable 'r'.

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

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

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

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 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 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

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