3s^2+9s-3=

Solution for 3s^2+9s-3= equation:

Simplifying
3s2 + 9s + -3 = 0

Reorder the terms:
-3 + 9s + 3s2 = 0

Solving
-3 + 9s + 3s2 = 0

Solving for variable 's'.

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

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

Simplifying
-1 + 3s + s2 = 0

Solving
-1 + 3s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3s + 1 + s2 = 0 + 1

Reorder the terms:
-1 + 1 + 3s + s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3s + s2 = 0 + 1
3s + s2 = 0 + 1

Combine like terms: 0 + 1 = 1
3s + s2 = 1

The s term is 3s.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3s + 2.25 + s2 = 1 + 2.25

Reorder the terms:
2.25 + 3s + s2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3s + s2 = 3.25

Factor a perfect square on the left side:
(s + 1.5)(s + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(s + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
s + 1.5 = 1.802775638

Simplifying
s + 1.5 = 1.802775638

Reorder the terms:
1.5 + s = 1.802775638

Solving
1.5 + s = 1.802775638

Solving for variable 's'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + s = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + s = 1.802775638 + -1.5
s = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
s = 0.302775638

Simplifying
s = 0.302775638

Subproblem 2
s + 1.5 = -1.802775638

Simplifying
s + 1.5 = -1.802775638

Reorder the terms:
1.5 + s = -1.802775638

Solving
1.5 + s = -1.802775638

Solving for variable 's'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + s = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + s = -1.802775638 + -1.5
s = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
s = -3.302775638

Simplifying
s = -3.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.302775638, -3.302775638}
Solution
s = {0.302775638, -3.302775638}