(s)=(53-5s+9)(2s+1)

Solution for (s)=(53-5s+9)(2s+1) equation:

Simplifying
(s) = (53 + -5s + 9)(2s + 1)
s = (53 + -5s + 9)(2s + 1)

Reorder the terms:
s = (53 + 9 + -5s)(2s + 1)

Combine like terms: 53 + 9 = 62
s = (62 + -5s)(2s + 1)

Reorder the terms:
s = (62 + -5s)(1 + 2s)

Multiply (62 + -5s) * (1 + 2s)
s = (62(1 + 2s) + -5s * (1 + 2s))
s = ((1 * 62 + 2s * 62) + -5s * (1 + 2s))
s = ((62 + 124s) + -5s * (1 + 2s))
s = (62 + 124s + (1 * -5s + 2s * -5s))
s = (62 + 124s + (-5s + -10s2))

Combine like terms: 124s + -5s = 119s
s = (62 + 119s + -10s2)

Solving
s = 62 + 119s + -10s2

Solving for variable 's'.

Reorder the terms:
-62 + s + -119s + 10s2 = 62 + 119s + -10s2 + -62 + -119s + 10s2

Combine like terms: s + -119s = -118s
-62 + -118s + 10s2 = 62 + 119s + -10s2 + -62 + -119s + 10s2

Reorder the terms:
-62 + -118s + 10s2 = 62 + -62 + 119s + -119s + -10s2 + 10s2

Combine like terms: 62 + -62 = 0
-62 + -118s + 10s2 = 0 + 119s + -119s + -10s2 + 10s2
-62 + -118s + 10s2 = 119s + -119s + -10s2 + 10s2

Combine like terms: 119s + -119s = 0
-62 + -118s + 10s2 = 0 + -10s2 + 10s2
-62 + -118s + 10s2 = -10s2 + 10s2

Combine like terms: -10s2 + 10s2 = 0
-62 + -118s + 10s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -59s + 5s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + -59s + 5s2)' equal to zero and attempt to solve:

Simplifying
-31 + -59s + 5s2 = 0

Solving
-31 + -59s + 5s2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-6.2 + -11.8s + s2 = 0

Move the constant term to the right:

Add '6.2' to each side of the equation.
-6.2 + -11.8s + 6.2 + s2 = 0 + 6.2

Reorder the terms:
-6.2 + 6.2 + -11.8s + s2 = 0 + 6.2

Combine like terms: -6.2 + 6.2 = 0.0
0.0 + -11.8s + s2 = 0 + 6.2
-11.8s + s2 = 0 + 6.2

Combine like terms: 0 + 6.2 = 6.2
-11.8s + s2 = 6.2

The s term is -11.8s.  Take half its coefficient (-5.9).
Square it (34.81) and add it to both sides.

Add '34.81' to each side of the equation.
-11.8s + 34.81 + s2 = 6.2 + 34.81

Reorder the terms:
34.81 + -11.8s + s2 = 6.2 + 34.81

Combine like terms: 6.2 + 34.81 = 41.01
34.81 + -11.8s + s2 = 41.01

Factor a perfect square on the left side:
(s + -5.9)(s + -5.9) = 41.01

Calculate the square root of the right side: 6.403905059

Break this problem into two subproblems by setting 
(s + -5.9) equal to 6.403905059 and -6.403905059.

Subproblem 1
s + -5.9 = 6.403905059

Simplifying
s + -5.9 = 6.403905059

Reorder the terms:
-5.9 + s = 6.403905059

Solving
-5.9 + s = 6.403905059

Solving for variable 's'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + s = 6.403905059 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + s = 6.403905059 + 5.9
s = 6.403905059 + 5.9

Combine like terms: 6.403905059 + 5.9 = 12.303905059
s = 12.303905059

Simplifying
s = 12.303905059

Subproblem 2
s + -5.9 = -6.403905059

Simplifying
s + -5.9 = -6.403905059

Reorder the terms:
-5.9 + s = -6.403905059

Solving
-5.9 + s = -6.403905059

Solving for variable 's'.

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

Add '5.9' to each side of the equation.
-5.9 + 5.9 + s = -6.403905059 + 5.9

Combine like terms: -5.9 + 5.9 = 0.0
0.0 + s = -6.403905059 + 5.9
s = -6.403905059 + 5.9

Combine like terms: -6.403905059 + 5.9 = -0.503905059
s = -0.503905059

Simplifying
s = -0.503905059

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {12.303905059, -0.503905059}
Solution
s = {12.303905059, -0.503905059}