-4(x+3)(x+3)+5=-8

Solution for -4(x+3)(x+3)+5=-8 equation:

Simplifying
-4(x + 3)(x + 3) + 5 = -8

Reorder the terms:
-4(3 + x)(x + 3) + 5 = -8

Reorder the terms:
-4(3 + x)(3 + x) + 5 = -8

Multiply (3 + x) * (3 + x)
-4(3(3 + x) + x(3 + x)) + 5 = -8
-4((3 * 3 + x * 3) + x(3 + x)) + 5 = -8
-4((9 + 3x) + x(3 + x)) + 5 = -8
-4(9 + 3x + (3 * x + x * x)) + 5 = -8
-4(9 + 3x + (3x + x2)) + 5 = -8

Combine like terms: 3x + 3x = 6x
-4(9 + 6x + x2) + 5 = -8
(9 * -4 + 6x * -4 + x2 * -4) + 5 = -8
(-36 + -24x + -4x2) + 5 = -8

Reorder the terms:
-36 + 5 + -24x + -4x2 = -8

Combine like terms: -36 + 5 = -31
-31 + -24x + -4x2 = -8

Solving
-31 + -24x + -4x2 = -8

Solving for variable 'x'.

Reorder the terms:
-31 + 8 + -24x + -4x2 = -8 + 8

Combine like terms: -31 + 8 = -23
-23 + -24x + -4x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-23 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(23 + 24x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(23 + 24x + 4x2)' equal to zero and attempt to solve:

Simplifying
23 + 24x + 4x2 = 0

Solving
23 + 24x + 4x2 = 0

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

Divide each side by '4'.
5.75 + 6x + x2 = 0

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + 6x + -5.75 + x2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + 6x + x2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + 6x + x2 = 0 + -5.75
6x + x2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
6x + x2 = -5.75

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -5.75 + 9

Reorder the terms:
9 + 6x + x2 = -5.75 + 9

Combine like terms: -5.75 + 9 = 3.25
9 + 6x + x2 = 3.25

Factor a perfect square on the left side:
(x + 3)(x + 3) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 3) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + 3 = 1.802775638

Simplifying
x + 3 = 1.802775638

Reorder the terms:
3 + x = 1.802775638

Solving
3 + x = 1.802775638

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.802775638 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.802775638 + -3
x = 1.802775638 + -3

Combine like terms: 1.802775638 + -3 = -1.197224362
x = -1.197224362

Simplifying
x = -1.197224362

Subproblem 2
x + 3 = -1.802775638

Simplifying
x + 3 = -1.802775638

Reorder the terms:
3 + x = -1.802775638

Solving
3 + x = -1.802775638

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.802775638 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.802775638 + -3
x = -1.802775638 + -3

Combine like terms: -1.802775638 + -3 = -4.802775638
x = -4.802775638

Simplifying
x = -4.802775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.197224362, -4.802775638}
Solution
x = {-1.197224362, -4.802775638}