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)) + (x + 3) = 63

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

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

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

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

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

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

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

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

Remove parenthesis around (3 + x)
3x + 2x2 + 3 + x = 63

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

Combine like terms: 3x + x = 4x
3 + 4x + 2x2 = 63

Solving
3 + 4x + 2x2 = 63

Solving for variable 'x'.

Reorder the terms:
3 + -63 + 4x + 2x2 = 63 + -63

Combine like terms: 3 + -63 = -60
-60 + 4x + 2x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-60 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 2x + x2 = 0

Solving
-30 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2x + x2 = 0 + 30
2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
2x + x2 = 30

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 30 + 1

Reorder the terms:
1 + 2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2x + x2 = 31

Factor a perfect square on the left side:
(x + 1)(x + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
x + 1 = 5.567764363

Simplifying
x + 1 = 5.567764363

Reorder the terms:
1 + x = 5.567764363

Solving
1 + x = 5.567764363

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.567764363 + -1
x = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
x = 4.567764363

Simplifying
x = 4.567764363

Subproblem 2
x + 1 = -5.567764363

Simplifying
x + 1 = -5.567764363

Reorder the terms:
1 + x = -5.567764363

Solving
1 + x = -5.567764363

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.567764363 + -1
x = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
x = -6.567764363

Simplifying
x = -6.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.567764363, -6.567764363}
Solution
x = {4.567764363, -6.567764363}