2(s+3)=s(4s-5)

Solution for 2(s+3)=s(4s-5) equation:

Simplifying
2(s + 3) = s(4s + -5)

Reorder the terms:
2(3 + s) = s(4s + -5)
(3 * 2 + s * 2) = s(4s + -5)
(6 + 2s) = s(4s + -5)

Reorder the terms:
6 + 2s = s(-5 + 4s)
6 + 2s = (-5 * s + 4s * s)
6 + 2s = (-5s + 4s2)

Solving
6 + 2s = -5s + 4s2

Solving for variable 's'.

Combine like terms: 2s + 5s = 7s
6 + 7s + -4s2 = -5s + 4s2 + 5s + -4s2

Reorder the terms:
6 + 7s + -4s2 = -5s + 5s + 4s2 + -4s2

Combine like terms: -5s + 5s = 0
6 + 7s + -4s2 = 0 + 4s2 + -4s2
6 + 7s + -4s2 = 4s2 + -4s2

Combine like terms: 4s2 + -4s2 = 0
6 + 7s + -4s2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.5 + -1.75s + s2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.75s + 1.5 + s2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.75s + s2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.75s + s2 = 0 + 1.5
-1.75s + s2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.75s + s2 = 1.5

The s term is -1.75s.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75s + 0.765625 + s2 = 1.5 + 0.765625

Reorder the terms:
0.765625 + -1.75s + s2 = 1.5 + 0.765625

Combine like terms: 1.5 + 0.765625 = 2.265625
0.765625 + -1.75s + s2 = 2.265625

Factor a perfect square on the left side:
(s + -0.875)(s + -0.875) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(s + -0.875) equal to 1.505199322 and -1.505199322.

Subproblem 1
s + -0.875 = 1.505199322

Simplifying
s + -0.875 = 1.505199322

Reorder the terms:
-0.875 + s = 1.505199322

Solving
-0.875 + s = 1.505199322

Solving for variable 's'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + s = 1.505199322 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + s = 1.505199322 + 0.875
s = 1.505199322 + 0.875

Combine like terms: 1.505199322 + 0.875 = 2.380199322
s = 2.380199322

Simplifying
s = 2.380199322

Subproblem 2
s + -0.875 = -1.505199322

Simplifying
s + -0.875 = -1.505199322

Reorder the terms:
-0.875 + s = -1.505199322

Solving
-0.875 + s = -1.505199322

Solving for variable 's'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + s = -1.505199322 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + s = -1.505199322 + 0.875
s = -1.505199322 + 0.875

Combine like terms: -1.505199322 + 0.875 = -0.630199322
s = -0.630199322

Simplifying
s = -0.630199322

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.380199322, -0.630199322}