2(s+3)+(4s-5)s=148

Solution for 2(s+3)+(4s-5)s=148 equation:

Simplifying
2(s + 3) + (4s + -5) * s = 148

Reorder the terms:
2(3 + s) + (4s + -5) * s = 148
(3 * 2 + s * 2) + (4s + -5) * s = 148
(6 + 2s) + (4s + -5) * s = 148

Reorder the terms:
6 + 2s + (-5 + 4s) * s = 148

Reorder the terms for easier multiplication:
6 + 2s + s(-5 + 4s) = 148
6 + 2s + (-5 * s + 4s * s) = 148
6 + 2s + (-5s + 4s2) = 148

Combine like terms: 2s + -5s = -3s
6 + -3s + 4s2 = 148

Solving
6 + -3s + 4s2 = 148

Solving for variable 's'.

Reorder the terms:
6 + -148 + -3s + 4s2 = 148 + -148

Combine like terms: 6 + -148 = -142
-142 + -3s + 4s2 = 148 + -148

Combine like terms: 148 + -148 = 0
-142 + -3s + 4s2 = 0

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

Divide each side by '4'.
-35.5 + -0.75s + s2 = 0

Move the constant term to the right:

Add '35.5' to each side of the equation.
-35.5 + -0.75s + 35.5 + s2 = 0 + 35.5

Reorder the terms:
-35.5 + 35.5 + -0.75s + s2 = 0 + 35.5

Combine like terms: -35.5 + 35.5 = 0.0
0.0 + -0.75s + s2 = 0 + 35.5
-0.75s + s2 = 0 + 35.5

Combine like terms: 0 + 35.5 = 35.5
-0.75s + s2 = 35.5

The s term is -0.75s.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75s + 0.140625 + s2 = 35.5 + 0.140625

Reorder the terms:
0.140625 + -0.75s + s2 = 35.5 + 0.140625

Combine like terms: 35.5 + 0.140625 = 35.640625
0.140625 + -0.75s + s2 = 35.640625

Factor a perfect square on the left side:
(s + -0.375)(s + -0.375) = 35.640625

Calculate the square root of the right side: 5.969976968

Break this problem into two subproblems by setting 
(s + -0.375) equal to 5.969976968 and -5.969976968.

Subproblem 1
s + -0.375 = 5.969976968

Simplifying
s + -0.375 = 5.969976968

Reorder the terms:
-0.375 + s = 5.969976968

Solving
-0.375 + s = 5.969976968

Solving for variable 's'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + s = 5.969976968 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + s = 5.969976968 + 0.375
s = 5.969976968 + 0.375

Combine like terms: 5.969976968 + 0.375 = 6.344976968
s = 6.344976968

Simplifying
s = 6.344976968

Subproblem 2
s + -0.375 = -5.969976968

Simplifying
s + -0.375 = -5.969976968

Reorder the terms:
-0.375 + s = -5.969976968

Solving
-0.375 + s = -5.969976968

Solving for variable 's'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + s = -5.969976968 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + s = -5.969976968 + 0.375
s = -5.969976968 + 0.375

Combine like terms: -5.969976968 + 0.375 = -5.594976968
s = -5.594976968

Simplifying
s = -5.594976968

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {6.344976968, -5.594976968}