5-x(x+3)=-(x+1)

Solution for 5-x(x+3)=-(x+1) equation:

Simplifying
5 + -1x(x + 3) = -1(x + 1)

Reorder the terms:
5 + -1x(3 + x) = -1(x + 1)
5 + (3 * -1x + x * -1x) = -1(x + 1)
5 + (-3x + -1x2) = -1(x + 1)

Reorder the terms:
5 + -3x + -1x2 = -1(1 + x)
5 + -3x + -1x2 = (1 * -1 + x * -1)
5 + -3x + -1x2 = (-1 + -1x)

Solving
5 + -3x + -1x2 = -1 + -1x

Solving for variable 'x'.

Reorder the terms:
5 + 1 + -3x + x + -1x2 = -1 + -1x + 1 + x

Combine like terms: 5 + 1 = 6
6 + -3x + x + -1x2 = -1 + -1x + 1 + x

Combine like terms: -3x + x = -2x
6 + -2x + -1x2 = -1 + -1x + 1 + x

Reorder the terms:
6 + -2x + -1x2 = -1 + 1 + -1x + x

Combine like terms: -1 + 1 = 0
6 + -2x + -1x2 = 0 + -1x + x
6 + -2x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
6 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 2x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 2x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2x + x2 = 0 + 6
2x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
2x + x2 = 6

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 = 6 + 1

Reorder the terms:
1 + 2x + x2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2x + x2 = 7

Factor a perfect square on the left side:
(x + 1)(x + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + 1 = 2.645751311

Simplifying
x + 1 = 2.645751311

Reorder the terms:
1 + x = 2.645751311

Solving
1 + x = 2.645751311

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 = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.645751311 + -1
x = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
x = 1.645751311

Simplifying
x = 1.645751311

Subproblem 2
x + 1 = -2.645751311

Simplifying
x + 1 = -2.645751311

Reorder the terms:
1 + x = -2.645751311

Solving
1 + x = -2.645751311

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 = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.645751311 + -1
x = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
x = -3.645751311

Simplifying
x = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.645751311, -3.645751311}