4s(2s+3)=4

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


Simplifying
4s(2s + 3) = 4

Reorder the terms:
4s(3 + 2s) = 4
(3 * 4s + 2s * 4s) = 4
(12s + 8s2) = 4

Solving
12s + 8s2 = 4

Solving for variable 's'.

Reorder the terms:
-4 + 12s + 8s2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 12s + 8s2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 3s + 2s2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 3s + 2s2)' equal to zero and attempt to solve:

Simplifying
-1 + 3s + 2s2 = 0

Solving
-1 + 3s + 2s2 = 0

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

Divide each side by '2'.
-0.5 + 1.5s + s2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.5s + 0.5 + s2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.5s + s2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.5s + s2 = 0 + 0.5
1.5s + s2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.5s + s2 = 0.5

The s term is 1.5s.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5s + 0.5625 + s2 = 0.5 + 0.5625

Reorder the terms:
0.5625 + 1.5s + s2 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + 1.5s + s2 = 1.0625

Factor a perfect square on the left side:
(s + 0.75)(s + 0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(s + 0.75) equal to 1.030776406 and -1.030776406.


Subproblem 1
s + 0.75 = 1.030776406

Simplifying
s + 0.75 = 1.030776406

Reorder the terms:
0.75 + s = 1.030776406

Solving
0.75 + s = 1.030776406

Solving for variable 's'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + s = 1.030776406 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + s = 1.030776406 + -0.75
s = 1.030776406 + -0.75

Combine like terms: 1.030776406 + -0.75 = 0.280776406
s = 0.280776406

Simplifying
s = 0.280776406


Subproblem 2
s + 0.75 = -1.030776406

Simplifying
s + 0.75 = -1.030776406

Reorder the terms:
0.75 + s = -1.030776406

Solving
0.75 + s = -1.030776406

Solving for variable 's'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + s = -1.030776406 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + s = -1.030776406 + -0.75
s = -1.030776406 + -0.75

Combine like terms: -1.030776406 + -0.75 = -1.780776406
s = -1.780776406

Simplifying
s = -1.780776406


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.280776406, -1.780776406}
Solution
s = {0.280776406, -1.780776406}

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