2s^2+4s=-6s+3

Solution for 2s^2+4s=-6s+3 equation:

Simplifying
2s2 + 4s = -6s + 3

Reorder the terms:
4s + 2s2 = -6s + 3

Reorder the terms:
4s + 2s2 = 3 + -6s

Solving
4s + 2s2 = 3 + -6s

Solving for variable 's'.

Reorder the terms:
-3 + 4s + 6s + 2s2 = 3 + -6s + -3 + 6s

Combine like terms: 4s + 6s = 10s
-3 + 10s + 2s2 = 3 + -6s + -3 + 6s

Reorder the terms:
-3 + 10s + 2s2 = 3 + -3 + -6s + 6s

Combine like terms: 3 + -3 = 0
-3 + 10s + 2s2 = 0 + -6s + 6s
-3 + 10s + 2s2 = -6s + 6s

Combine like terms: -6s + 6s = 0
-3 + 10s + 2s2 = 0

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

Divide each side by '2'.
-1.5 + 5s + s2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 5s + 1.5 + s2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 5s + s2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 5s + s2 = 0 + 1.5
5s + s2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
5s + s2 = 1.5

The s term is 5s.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5s + 6.25 + s2 = 1.5 + 6.25

Reorder the terms:
6.25 + 5s + s2 = 1.5 + 6.25

Combine like terms: 1.5 + 6.25 = 7.75
6.25 + 5s + s2 = 7.75

Factor a perfect square on the left side:
(s + 2.5)(s + 2.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(s + 2.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
s + 2.5 = 2.783882181

Simplifying
s + 2.5 = 2.783882181

Reorder the terms:
2.5 + s = 2.783882181

Solving
2.5 + s = 2.783882181

Solving for variable 's'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + s = 2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + s = 2.783882181 + -2.5
s = 2.783882181 + -2.5

Combine like terms: 2.783882181 + -2.5 = 0.283882181
s = 0.283882181

Simplifying
s = 0.283882181

Subproblem 2
s + 2.5 = -2.783882181

Simplifying
s + 2.5 = -2.783882181

Reorder the terms:
2.5 + s = -2.783882181

Solving
2.5 + s = -2.783882181

Solving for variable 's'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + s = -2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + s = -2.783882181 + -2.5
s = -2.783882181 + -2.5

Combine like terms: -2.783882181 + -2.5 = -5.283882181
s = -5.283882181

Simplifying
s = -5.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.283882181, -5.283882181}