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

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

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

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

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

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

Combine like terms: 2s + -5s = -3s
(-2 + -3s + 5s2) = 2s + 1

Reorder the terms:
-2 + -3s + 5s2 = 1 + 2s

Solving
-2 + -3s + 5s2 = 1 + 2s

Solving for variable 's'.

Reorder the terms:
-2 + -1 + -3s + -2s + 5s2 = 1 + 2s + -1 + -2s

Combine like terms: -2 + -1 = -3
-3 + -3s + -2s + 5s2 = 1 + 2s + -1 + -2s

Combine like terms: -3s + -2s = -5s
-3 + -5s + 5s2 = 1 + 2s + -1 + -2s

Reorder the terms:
-3 + -5s + 5s2 = 1 + -1 + 2s + -2s

Combine like terms: 1 + -1 = 0
-3 + -5s + 5s2 = 0 + 2s + -2s
-3 + -5s + 5s2 = 2s + -2s

Combine like terms: 2s + -2s = 0
-3 + -5s + 5s2 = 0

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

Divide each side by '5'.
-0.6 + -1s + s2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1s + 0.6 + s2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1s + s2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1s + s2 = 0 + 0.6
-1s + s2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1s + s2 = 0.6

The s term is -1s.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1s + 0.25 + s2 = 0.6 + 0.25

Reorder the terms:
0.25 + -1s + s2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + -1s + s2 = 0.85

Factor a perfect square on the left side:
(s + -0.5)(s + -0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(s + -0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
s + -0.5 = 0.921954446

Simplifying
s + -0.5 = 0.921954446

Reorder the terms:
-0.5 + s = 0.921954446

Solving
-0.5 + s = 0.921954446

Solving for variable 's'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + s = 0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + s = 0.921954446 + 0.5
s = 0.921954446 + 0.5

Combine like terms: 0.921954446 + 0.5 = 1.421954446
s = 1.421954446

Simplifying
s = 1.421954446

Subproblem 2
s + -0.5 = -0.921954446

Simplifying
s + -0.5 = -0.921954446

Reorder the terms:
-0.5 + s = -0.921954446

Solving
-0.5 + s = -0.921954446

Solving for variable 's'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + s = -0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + s = -0.921954446 + 0.5
s = -0.921954446 + 0.5

Combine like terms: -0.921954446 + 0.5 = -0.421954446
s = -0.421954446

Simplifying
s = -0.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {1.421954446, -0.421954446}