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

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

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

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

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

Combine like terms: 6x + -6x = 0
3x + -1(-36 + 0 + x2) + -5(1 + 5x) = 1 + 3x
3x + -1(-36 + x2) + -5(1 + 5x) = 1 + 3x
3x + (-36 * -1 + x2 * -1) + -5(1 + 5x) = 1 + 3x
3x + (36 + -1x2) + -5(1 + 5x) = 1 + 3x
3x + 36 + -1x2 + (1 * -5 + 5x * -5) = 1 + 3x
3x + 36 + -1x2 + (-5 + -25x) = 1 + 3x

Reorder the terms:
36 + -5 + 3x + -25x + -1x2 = 1 + 3x

Combine like terms: 36 + -5 = 31
31 + 3x + -25x + -1x2 = 1 + 3x

Combine like terms: 3x + -25x = -22x
31 + -22x + -1x2 = 1 + 3x

Solving
31 + -22x + -1x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
31 + -1 + -22x + -3x + -1x2 = 1 + 3x + -1 + -3x

Combine like terms: 31 + -1 = 30
30 + -22x + -3x + -1x2 = 1 + 3x + -1 + -3x

Combine like terms: -22x + -3x = -25x
30 + -25x + -1x2 = 1 + 3x + -1 + -3x

Reorder the terms:
30 + -25x + -1x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
30 + -25x + -1x2 = 0 + 3x + -3x
30 + -25x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
30 + -25x + -1x2 = 0

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

Divide each side by '-1'.
-30 + 25x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 25x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 25x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 25x + x2 = 0 + 30
25x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
25x + x2 = 30

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 30 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 30 + 156.25

Combine like terms: 30 + 156.25 = 186.25
156.25 + 25x + x2 = 186.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.647344064 and -13.647344064.

Subproblem 1
x + 12.5 = 13.647344064

Simplifying
x + 12.5 = 13.647344064

Reorder the terms:
12.5 + x = 13.647344064

Solving
12.5 + x = 13.647344064

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 13.647344064 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 13.647344064 + -12.5
x = 13.647344064 + -12.5

Combine like terms: 13.647344064 + -12.5 = 1.147344064
x = 1.147344064

Simplifying
x = 1.147344064

Subproblem 2
x + 12.5 = -13.647344064

Simplifying
x + 12.5 = -13.647344064

Reorder the terms:
12.5 + x = -13.647344064

Solving
12.5 + x = -13.647344064

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -13.647344064 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -13.647344064 + -12.5
x = -13.647344064 + -12.5

Combine like terms: -13.647344064 + -12.5 = -26.147344064
x = -26.147344064

Simplifying
x = -26.147344064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.147344064, -26.147344064}