3x-(6+x)(x-6)-5(1+x)=1+x

Solution for 3x-(6+x)(x-6)-5(1+x)=1+x equation:

Simplifying
3x + -1(6 + x)(x + -6) + -5(1 + x) = 1 + x

Reorder the terms:
3x + -1(6 + x)(-6 + x) + -5(1 + x) = 1 + x

Multiply (6 + x) * (-6 + x)
3x + -1(6(-6 + x) + x(-6 + x)) + -5(1 + x) = 1 + x
3x + -1((-6 * 6 + x * 6) + x(-6 + x)) + -5(1 + x) = 1 + x
3x + -1((-36 + 6x) + x(-6 + x)) + -5(1 + x) = 1 + x
3x + -1(-36 + 6x + (-6 * x + x * x)) + -5(1 + x) = 1 + x
3x + -1(-36 + 6x + (-6x + x2)) + -5(1 + x) = 1 + x

Combine like terms: 6x + -6x = 0
3x + -1(-36 + 0 + x2) + -5(1 + x) = 1 + x
3x + -1(-36 + x2) + -5(1 + x) = 1 + x
3x + (-36 * -1 + x2 * -1) + -5(1 + x) = 1 + x
3x + (36 + -1x2) + -5(1 + x) = 1 + x
3x + 36 + -1x2 + (1 * -5 + x * -5) = 1 + x
3x + 36 + -1x2 + (-5 + -5x) = 1 + x

Reorder the terms:
36 + -5 + 3x + -5x + -1x2 = 1 + x

Combine like terms: 36 + -5 = 31
31 + 3x + -5x + -1x2 = 1 + x

Combine like terms: 3x + -5x = -2x
31 + -2x + -1x2 = 1 + x

Solving
31 + -2x + -1x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
31 + -1 + -2x + -1x + -1x2 = 1 + x + -1 + -1x

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

Combine like terms: -2x + -1x = -3x
30 + -3x + -1x2 = 1 + x + -1 + -1x

Reorder the terms:
30 + -3x + -1x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
30 + -3x + -1x2 = 0 + x + -1x
30 + -3x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
30 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-30 + 3x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 3x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3x + x2 = 0 + 30
3x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
3x + x2 = 30

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 30 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3x + x2 = 32.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 1.5 = 5.678908346

Simplifying
x + 1.5 = 5.678908346

Reorder the terms:
1.5 + x = 5.678908346

Solving
1.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.678908346 + -1.5
x = 5.678908346 + -1.5

Combine like terms: 5.678908346 + -1.5 = 4.178908346
x = 4.178908346

Simplifying
x = 4.178908346

Subproblem 2
x + 1.5 = -5.678908346

Simplifying
x + 1.5 = -5.678908346

Reorder the terms:
1.5 + x = -5.678908346

Solving
1.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.678908346 + -1.5
x = -5.678908346 + -1.5

Combine like terms: -5.678908346 + -1.5 = -7.178908346
x = -7.178908346

Simplifying
x = -7.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.178908346, -7.178908346}