4s(s+3)-2(1-s)=

Solution for 4s(s+3)-2(1-s)= equation:

Simplifying
4s(s + 3) + -2(1 + -1s) = 0

Reorder the terms:
4s(3 + s) + -2(1 + -1s) = 0
(3 * 4s + s * 4s) + -2(1 + -1s) = 0
(12s + 4s2) + -2(1 + -1s) = 0
12s + 4s2 + (1 * -2 + -1s * -2) = 0
12s + 4s2 + (-2 + 2s) = 0

Reorder the terms:
-2 + 12s + 2s + 4s2 = 0

Combine like terms: 12s + 2s = 14s
-2 + 14s + 4s2 = 0

Solving
-2 + 14s + 4s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 7s + 2s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 7s + 2s2)' equal to zero and attempt to solve:

Simplifying
-1 + 7s + 2s2 = 0

Solving
-1 + 7s + 2s2 = 0

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

Divide each side by '2'.
-0.5 + 3.5s + s2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3.5s + 0.5 + s2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3.5s + s2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3.5s + s2 = 0 + 0.5
3.5s + s2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3.5s + s2 = 0.5

The s term is 3.5s.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5s + 3.0625 + s2 = 0.5 + 3.0625

Reorder the terms:
3.0625 + 3.5s + s2 = 0.5 + 3.0625

Combine like terms: 0.5 + 3.0625 = 3.5625
3.0625 + 3.5s + s2 = 3.5625

Factor a perfect square on the left side:
(s + 1.75)(s + 1.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(s + 1.75) equal to 1.887458609 and -1.887458609.

Subproblem 1
s + 1.75 = 1.887458609

Simplifying
s + 1.75 = 1.887458609

Reorder the terms:
1.75 + s = 1.887458609

Solving
1.75 + s = 1.887458609

Solving for variable 's'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + s = 1.887458609 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + s = 1.887458609 + -1.75
s = 1.887458609 + -1.75

Combine like terms: 1.887458609 + -1.75 = 0.137458609
s = 0.137458609

Simplifying
s = 0.137458609

Subproblem 2
s + 1.75 = -1.887458609

Simplifying
s + 1.75 = -1.887458609

Reorder the terms:
1.75 + s = -1.887458609

Solving
1.75 + s = -1.887458609

Solving for variable 's'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + s = -1.887458609 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + s = -1.887458609 + -1.75
s = -1.887458609 + -1.75

Combine like terms: -1.887458609 + -1.75 = -3.637458609
s = -3.637458609

Simplifying
s = -3.637458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.137458609, -3.637458609}
Solution
s = {0.137458609, -3.637458609}