4s-s(s+4)=2(2s+3)+9

Solution for 4s-s(s+4)=2(2s+3)+9 equation:

Simplifying
4s + -1s(s + 4) = 2(2s + 3) + 9

Reorder the terms:
4s + -1s(4 + s) = 2(2s + 3) + 9
4s + (4 * -1s + s * -1s) = 2(2s + 3) + 9
4s + (-4s + -1s2) = 2(2s + 3) + 9

Combine like terms: 4s + -4s = 0
0 + -1s2 = 2(2s + 3) + 9
-1s2 = 2(2s + 3) + 9

Reorder the terms:
-1s2 = 2(3 + 2s) + 9
-1s2 = (3 * 2 + 2s * 2) + 9
-1s2 = (6 + 4s) + 9

Reorder the terms:
-1s2 = 6 + 9 + 4s

Combine like terms: 6 + 9 = 15
-1s2 = 15 + 4s

Solving
-1s2 = 15 + 4s

Solving for variable 's'.

Reorder the terms:
-15 + -4s + -1s2 = 15 + 4s + -15 + -4s

Reorder the terms:
-15 + -4s + -1s2 = 15 + -15 + 4s + -4s

Combine like terms: 15 + -15 = 0
-15 + -4s + -1s2 = 0 + 4s + -4s
-15 + -4s + -1s2 = 4s + -4s

Combine like terms: 4s + -4s = 0
-15 + -4s + -1s2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 4s + s2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(15 + 4s + s2)' equal to zero and attempt to solve:

Simplifying
15 + 4s + s2 = 0

Solving
15 + 4s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 4s + -15 + s2 = 0 + -15

Reorder the terms:
15 + -15 + 4s + s2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 4s + s2 = 0 + -15
4s + s2 = 0 + -15

Combine like terms: 0 + -15 = -15
4s + s2 = -15

The s term is 4s.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4s + 4 + s2 = -15 + 4

Reorder the terms:
4 + 4s + s2 = -15 + 4

Combine like terms: -15 + 4 = -11
4 + 4s + s2 = -11

Factor a perfect square on the left side:
(s + 2)(s + 2) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.