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

Solution for (x-1)=3x(4x+6) equation:

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

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

Remove parenthesis around (-1 + x)
-1 + x = 3x(4x + 6)

Reorder the terms:
-1 + x = 3x(6 + 4x)
-1 + x = (6 * 3x + 4x * 3x)
-1 + x = (18x + 12x2)

Solving
-1 + x = 18x + 12x2

Solving for variable 'x'.

Combine like terms: x + -18x = -17x
-1 + -17x + -12x2 = 18x + 12x2 + -18x + -12x2

Reorder the terms:
-1 + -17x + -12x2 = 18x + -18x + 12x2 + -12x2

Combine like terms: 18x + -18x = 0
-1 + -17x + -12x2 = 0 + 12x2 + -12x2
-1 + -17x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-1 + -17x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 17x + 12x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 17x + 12x2)' equal to zero and attempt to solve:

Simplifying
1 + 17x + 12x2 = 0

Solving
1 + 17x + 12x2 = 0

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

Divide each side by '12'.
0.08333333333 + 1.416666667x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + 1.416666667x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + 1.416666667x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + 1.416666667x + x2 = 0 + -0.08333333333
1.416666667x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
1.416666667x + x2 = -0.08333333333

The x term is 1.416666667x.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667x + 0.5017361113 + x2 = -0.08333333333 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667x + x2 = -0.08333333333 + 0.5017361113

Combine like terms: -0.08333333333 + 0.5017361113 = 0.41840277797
0.5017361113 + 1.416666667x + x2 = 0.41840277797

Factor a perfect square on the left side:
(x + 0.7083333335)(x + 0.7083333335) = 0.41840277797

Calculate the square root of the right side: 0.646840612

Break this problem into two subproblems by setting 
(x + 0.7083333335) equal to 0.646840612 and -0.646840612.

Subproblem 1
x + 0.7083333335 = 0.646840612

Simplifying
x + 0.7083333335 = 0.646840612

Reorder the terms:
0.7083333335 + x = 0.646840612

Solving
0.7083333335 + x = 0.646840612

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = 0.646840612 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = 0.646840612 + -0.7083333335
x = 0.646840612 + -0.7083333335

Combine like terms: 0.646840612 + -0.7083333335 = -0.0614927215
x = -0.0614927215

Simplifying
x = -0.0614927215

Subproblem 2
x + 0.7083333335 = -0.646840612

Simplifying
x + 0.7083333335 = -0.646840612

Reorder the terms:
0.7083333335 + x = -0.646840612

Solving
0.7083333335 + x = -0.646840612

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = -0.646840612 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = -0.646840612 + -0.7083333335
x = -0.646840612 + -0.7083333335

Combine like terms: -0.646840612 + -0.7083333335 = -1.3551739455
x = -1.3551739455

Simplifying
x = -1.3551739455

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.0614927215, -1.3551739455}
Solution
x = {-0.0614927215, -1.3551739455}