s(5+s)=84

Solution for s(5+s)=84 equation:

Simplifying
s(5 + s) = 84
(5 * s + s * s) = 84
(5s + s2) = 84

Solving
5s + s2 = 84

Solving for variable 's'.

Reorder the terms:
-84 + 5s + s2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 5s + s2 = 0

Factor a trinomial.
(-12 + -1s)(7 + -1s) = 0

Subproblem 1
Set the factor '(-12 + -1s)' equal to zero and attempt to solve:

Simplifying
-12 + -1s = 0

Solving
-12 + -1s = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1s = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1s = 0 + 12
-1s = 0 + 12

Combine like terms: 0 + 12 = 12
-1s = 12

Divide each side by '-1'.
s = -12

Simplifying
s = -12
Subproblem 2
Set the factor '(7 + -1s)' equal to zero and attempt to solve:

Simplifying
7 + -1s = 0

Solving
7 + -1s = 0

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

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

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

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

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

Simplifying
s = 7
Solution
s = {-12, 7}