=-3(x+2)(x+2)+5

Solution for =-3(x+2)(x+2)+5 equation:

Simplifying
0 = -3(x + 2)(x + 2) + 5

Reorder the terms:
0 = -3(2 + x)(x + 2) + 5

Reorder the terms:
0 = -3(2 + x)(2 + x) + 5

Multiply (2 + x) * (2 + x)
0 = -3(2(2 + x) + x(2 + x)) + 5
0 = -3((2 * 2 + x * 2) + x(2 + x)) + 5
0 = -3((4 + 2x) + x(2 + x)) + 5
0 = -3(4 + 2x + (2 * x + x * x)) + 5
0 = -3(4 + 2x + (2x + x2)) + 5

Combine like terms: 2x + 2x = 4x
0 = -3(4 + 4x + x2) + 5
0 = (4 * -3 + 4x * -3 + x2 * -3) + 5
0 = (-12 + -12x + -3x2) + 5

Reorder the terms:
0 = -12 + 5 + -12x + -3x2

Combine like terms: -12 + 5 = -7
0 = -7 + -12x + -3x2

Solving
0 = -7 + -12x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + 12x + 3x2 = -7 + -12x + -3x2 + 7 + 12x + 3x2

Reorder the terms:
7 + 12x + 3x2 = -7 + 7 + -12x + 12x + -3x2 + 3x2

Combine like terms: -7 + 7 = 0
7 + 12x + 3x2 = 0 + -12x + 12x + -3x2 + 3x2
7 + 12x + 3x2 = -12x + 12x + -3x2 + 3x2

Combine like terms: -12x + 12x = 0
7 + 12x + 3x2 = 0 + -3x2 + 3x2
7 + 12x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
7 + 12x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 4x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 4x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + -2.333333333
4x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
4x + x2 = -2.333333333

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

Add '4' to each side of the equation.
4x + 4 + x2 = -2.333333333 + 4

Reorder the terms:
4 + 4x + x2 = -2.333333333 + 4

Combine like terms: -2.333333333 + 4 = 1.666666667
4 + 4x + x2 = 1.666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 1.666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + 2) equal to 1.290994449 and -1.290994449.

Subproblem 1
x + 2 = 1.290994449

Simplifying
x + 2 = 1.290994449

Reorder the terms:
2 + x = 1.290994449

Solving
2 + x = 1.290994449

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.290994449 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.290994449 + -2
x = 1.290994449 + -2

Combine like terms: 1.290994449 + -2 = -0.709005551
x = -0.709005551

Simplifying
x = -0.709005551

Subproblem 2
x + 2 = -1.290994449

Simplifying
x + 2 = -1.290994449

Reorder the terms:
2 + x = -1.290994449

Solving
2 + x = -1.290994449

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.290994449 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.290994449 + -2
x = -1.290994449 + -2

Combine like terms: -1.290994449 + -2 = -3.290994449
x = -3.290994449

Simplifying
x = -3.290994449

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.709005551, -3.290994449}