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

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

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

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

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

Multiply (-1 + 3x) * (3 + x)
(-1(3 + x) + 3x * (3 + x)) = x(1 + 6x)
((3 * -1 + x * -1) + 3x * (3 + x)) = x(1 + 6x)
((-3 + -1x) + 3x * (3 + x)) = x(1 + 6x)
(-3 + -1x + (3 * 3x + x * 3x)) = x(1 + 6x)
(-3 + -1x + (9x + 3x2)) = x(1 + 6x)

Combine like terms: -1x + 9x = 8x
(-3 + 8x + 3x2) = x(1 + 6x)
-3 + 8x + 3x2 = (1 * x + 6x * x)
-3 + 8x + 3x2 = (1x + 6x2)

Solving
-3 + 8x + 3x2 = 1x + 6x2

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + -1x + 3x2 + -6x2 = 1x + 6x2 + -1x + -6x2

Combine like terms: 8x + -1x = 7x
-3 + 7x + 3x2 + -6x2 = 1x + 6x2 + -1x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
-3 + 7x + -3x2 = 1x + 6x2 + -1x + -6x2

Reorder the terms:
-3 + 7x + -3x2 = 1x + -1x + 6x2 + -6x2

Combine like terms: 1x + -1x = 0
-3 + 7x + -3x2 = 0 + 6x2 + -6x2
-3 + 7x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-3 + 7x + -3x2 = 0

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

Divide each side by '-3'.
1 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.333333333x + x2 = 0 + -1
-2.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.333333333x + x2 = -1

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -1 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -1 + 1.361111112

Combine like terms: -1 + 1.361111112 = 0.361111112
1.361111112 + -2.333333333x + x2 = 0.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 0.361111112

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 0.600925213 and -0.600925213.

Subproblem 1
x + -1.166666667 = 0.600925213

Simplifying
x + -1.166666667 = 0.600925213

Reorder the terms:
-1.166666667 + x = 0.600925213

Solving
-1.166666667 + x = 0.600925213

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 0.600925213 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 0.600925213 + 1.166666667
x = 0.600925213 + 1.166666667

Combine like terms: 0.600925213 + 1.166666667 = 1.76759188
x = 1.76759188

Simplifying
x = 1.76759188

Subproblem 2
x + -1.166666667 = -0.600925213

Simplifying
x + -1.166666667 = -0.600925213

Reorder the terms:
-1.166666667 + x = -0.600925213

Solving
-1.166666667 + x = -0.600925213

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -0.600925213 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -0.600925213 + 1.166666667
x = -0.600925213 + 1.166666667

Combine like terms: -0.600925213 + 1.166666667 = 0.565741454
x = 0.565741454

Simplifying
x = 0.565741454

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.76759188, 0.565741454}