x((x+1)+(x+2))-(x+3)=63

Solution for x((x+1)+(x+2))-(x+3)=63 equation:

Simplifying
x((x + 1) + (x + 2)) + -1(x + 3) = 63

Reorder the terms:
x((1 + x) + (x + 2)) + -1(x + 3) = 63

Remove parenthesis around (1 + x)
x(1 + x + (x + 2)) + -1(x + 3) = 63

Reorder the terms:
x(1 + x + (2 + x)) + -1(x + 3) = 63

Remove parenthesis around (2 + x)
x(1 + x + 2 + x) + -1(x + 3) = 63

Reorder the terms:
x(1 + 2 + x + x) + -1(x + 3) = 63

Combine like terms: 1 + 2 = 3
x(3 + x + x) + -1(x + 3) = 63

Combine like terms: x + x = 2x
x(3 + 2x) + -1(x + 3) = 63
(3 * x + 2x * x) + -1(x + 3) = 63
(3x + 2x2) + -1(x + 3) = 63

Reorder the terms:
3x + 2x2 + -1(3 + x) = 63
3x + 2x2 + (3 * -1 + x * -1) = 63
3x + 2x2 + (-3 + -1x) = 63

Reorder the terms:
-3 + 3x + -1x + 2x2 = 63

Combine like terms: 3x + -1x = 2x
-3 + 2x + 2x2 = 63

Solving
-3 + 2x + 2x2 = 63

Solving for variable 'x'.

Reorder the terms:
-3 + -63 + 2x + 2x2 = 63 + -63

Combine like terms: -3 + -63 = -66
-66 + 2x + 2x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-66 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-33 + x + x2)' equal to zero and attempt to solve:

Simplifying
-33 + x + x2 = 0

Solving
-33 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + x + x2 = 0 + 33
x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
x + x2 = 33

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 33 + 0.25

Reorder the terms:
0.25 + x + x2 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + x + x2 = 33.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
x + 0.5 = 5.766281297

Simplifying
x + 0.5 = 5.766281297

Reorder the terms:
0.5 + x = 5.766281297

Solving
0.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.766281297 + -0.5
x = 5.766281297 + -0.5

Combine like terms: 5.766281297 + -0.5 = 5.266281297
x = 5.266281297

Simplifying
x = 5.266281297

Subproblem 2
x + 0.5 = -5.766281297

Simplifying
x + 0.5 = -5.766281297

Reorder the terms:
0.5 + x = -5.766281297

Solving
0.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.766281297 + -0.5
x = -5.766281297 + -0.5

Combine like terms: -5.766281297 + -0.5 = -6.266281297
x = -6.266281297

Simplifying
x = -6.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.266281297, -6.266281297}
Solution
x = {5.266281297, -6.266281297}