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

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

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

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

Reorder the terms for easier multiplication:
5x = (6x + 1)(x + -5)

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

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

Multiply (1 + 6x) * (-5 + x)
5x = (1(-5 + x) + 6x * (-5 + x))
5x = ((-5 * 1 + x * 1) + 6x * (-5 + x))
5x = ((-5 + 1x) + 6x * (-5 + x))
5x = (-5 + 1x + (-5 * 6x + x * 6x))
5x = (-5 + 1x + (-30x + 6x2))

Combine like terms: 1x + -30x = -29x
5x = (-5 + -29x + 6x2)

Solving
5x = -5 + -29x + 6x2

Solving for variable 'x'.

Reorder the terms:
5 + 5x + 29x + -6x2 = -5 + -29x + 6x2 + 5 + 29x + -6x2

Combine like terms: 5x + 29x = 34x
5 + 34x + -6x2 = -5 + -29x + 6x2 + 5 + 29x + -6x2

Reorder the terms:
5 + 34x + -6x2 = -5 + 5 + -29x + 29x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
5 + 34x + -6x2 = 0 + -29x + 29x + 6x2 + -6x2
5 + 34x + -6x2 = -29x + 29x + 6x2 + -6x2

Combine like terms: -29x + 29x = 0
5 + 34x + -6x2 = 0 + 6x2 + -6x2
5 + 34x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 34x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.8333333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -5.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -5.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -5.666666667x + x2 = 0 + 0.8333333333
-5.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-5.666666667x + x2 = 0.8333333333

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 0.8333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 0.8333333333 + 8.027777782

Combine like terms: 0.8333333333 + 8.027777782 = 8.8611111153
8.027777782 + -5.666666667x + x2 = 8.8611111153

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 8.8611111153

Calculate the square root of the right side: 2.976761851

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.976761851 and -2.976761851.

Subproblem 1
x + -2.833333334 = 2.976761851

Simplifying
x + -2.833333334 = 2.976761851

Reorder the terms:
-2.833333334 + x = 2.976761851

Solving
-2.833333334 + x = 2.976761851

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.976761851 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.976761851 + 2.833333334
x = 2.976761851 + 2.833333334

Combine like terms: 2.976761851 + 2.833333334 = 5.810095185
x = 5.810095185

Simplifying
x = 5.810095185

Subproblem 2
x + -2.833333334 = -2.976761851

Simplifying
x + -2.833333334 = -2.976761851

Reorder the terms:
-2.833333334 + x = -2.976761851

Solving
-2.833333334 + x = -2.976761851

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.976761851 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.976761851 + 2.833333334
x = -2.976761851 + 2.833333334

Combine like terms: -2.976761851 + 2.833333334 = -0.143428517
x = -0.143428517

Simplifying
x = -0.143428517

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.810095185, -0.143428517}