x-x(x+4x-3-6x)-x=60

Solution for x-x(x+4x-3-6x)-x=60 equation:

Simplifying
x + -1x(x + 4x + -3 + -6x) + -1x = 60

Reorder the terms:
x + -1x(-3 + x + 4x + -6x) + -1x = 60

Combine like terms: x + 4x = 5x
x + -1x(-3 + 5x + -6x) + -1x = 60

Combine like terms: 5x + -6x = -1x
x + -1x(-3 + -1x) + -1x = 60
x + (-3 * -1x + -1x * -1x) + -1x = 60
x + (3x + 1x2) + -1x = 60

Reorder the terms:
x + 3x + -1x + 1x2 = 60

Combine like terms: x + 3x = 4x
4x + -1x + 1x2 = 60

Combine like terms: 4x + -1x = 3x
3x + 1x2 = 60

Solving
3x + 1x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 3x + 1x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 3x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 3x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 3x + x2 = 0 + 60
3x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
3x + x2 = 60

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 = 60 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 60 + 2.25

Combine like terms: 60 + 2.25 = 62.25
2.25 + 3x + x2 = 62.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
x + 1.5 = 7.889866919

Simplifying
x + 1.5 = 7.889866919

Reorder the terms:
1.5 + x = 7.889866919

Solving
1.5 + x = 7.889866919

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 = 7.889866919 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 7.889866919 + -1.5
x = 7.889866919 + -1.5

Combine like terms: 7.889866919 + -1.5 = 6.389866919
x = 6.389866919

Simplifying
x = 6.389866919

Subproblem 2
x + 1.5 = -7.889866919

Simplifying
x + 1.5 = -7.889866919

Reorder the terms:
1.5 + x = -7.889866919

Solving
1.5 + x = -7.889866919

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 = -7.889866919 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -7.889866919 + -1.5
x = -7.889866919 + -1.5

Combine like terms: -7.889866919 + -1.5 = -9.389866919
x = -9.389866919

Simplifying
x = -9.389866919

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.389866919, -9.389866919}