(-x-3)(3x-3)=4

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Solution for (-x-3)(3x-3)=4 equation: 


Simplifying
(-1x + -3)(3x + -3) = 4

Reorder the terms:
(-3 + -1x)(3x + -3) = 4

Reorder the terms:
(-3 + -1x)(-3 + 3x) = 4

Multiply (-3 + -1x) * (-3 + 3x)
(-3(-3 + 3x) + -1x * (-3 + 3x)) = 4
((-3 * -3 + 3x * -3) + -1x * (-3 + 3x)) = 4
((9 + -9x) + -1x * (-3 + 3x)) = 4
(9 + -9x + (-3 * -1x + 3x * -1x)) = 4
(9 + -9x + (3x + -3x2)) = 4

Combine like terms: -9x + 3x = -6x
(9 + -6x + -3x2) = 4

Solving
9 + -6x + -3x2 = 4

Solving for variable 'x'.

Reorder the terms:
9 + -4 + -6x + -3x2 = 4 + -4

Combine like terms: 9 + -4 = 5
5 + -6x + -3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
5 + -6x + -3x2 = 0

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

Divide each side by '-3'.
-1.666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.666666667
2x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2x + x2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + 2x + x2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + 2x + x2 = 2.666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(x + 1) equal to 1.632993162 and -1.632993162.


Subproblem 1
x + 1 = 1.632993162

Simplifying
x + 1 = 1.632993162

Reorder the terms:
1 + x = 1.632993162

Solving
1 + x = 1.632993162

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 = 1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.632993162 + -1
x = 1.632993162 + -1

Combine like terms: 1.632993162 + -1 = 0.632993162
x = 0.632993162

Simplifying
x = 0.632993162


Subproblem 2
x + 1 = -1.632993162

Simplifying
x + 1 = -1.632993162

Reorder the terms:
1 + x = -1.632993162

Solving
1 + x = -1.632993162

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 = -1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.632993162 + -1
x = -1.632993162 + -1

Combine like terms: -1.632993162 + -1 = -2.632993162
x = -2.632993162

Simplifying
x = -2.632993162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.632993162, -2.632993162}

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