r(5+r)=14

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

Simplifying
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.
(-7 + -1r)(2 + -1r) = 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 + -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
Solution
r = {-7, 2}