(3x+2)(5x-1)-1=3x(x-1)

Solution for (3x+2)(5x-1)-1=3x(x-1) equation:

Simplifying
(3x + 2)(5x + -1) + -1 = 3x(x + -1)

Reorder the terms:
(2 + 3x)(5x + -1) + -1 = 3x(x + -1)

Reorder the terms:
(2 + 3x)(-1 + 5x) + -1 = 3x(x + -1)

Multiply (2 + 3x) * (-1 + 5x)
(2(-1 + 5x) + 3x * (-1 + 5x)) + -1 = 3x(x + -1)
((-1 * 2 + 5x * 2) + 3x * (-1 + 5x)) + -1 = 3x(x + -1)
((-2 + 10x) + 3x * (-1 + 5x)) + -1 = 3x(x + -1)
(-2 + 10x + (-1 * 3x + 5x * 3x)) + -1 = 3x(x + -1)
(-2 + 10x + (-3x + 15x2)) + -1 = 3x(x + -1)

Combine like terms: 10x + -3x = 7x
(-2 + 7x + 15x2) + -1 = 3x(x + -1)

Reorder the terms:
-2 + -1 + 7x + 15x2 = 3x(x + -1)

Combine like terms: -2 + -1 = -3
-3 + 7x + 15x2 = 3x(x + -1)

Reorder the terms:
-3 + 7x + 15x2 = 3x(-1 + x)
-3 + 7x + 15x2 = (-1 * 3x + x * 3x)
-3 + 7x + 15x2 = (-3x + 3x2)

Solving
-3 + 7x + 15x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
-3 + 7x + 3x + 15x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 7x + 3x = 10x
-3 + 10x + 15x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 15x2 + -3x2 = 12x2
-3 + 10x + 12x2 = -3x + 3x2 + 3x + -3x2

Reorder the terms:
-3 + 10x + 12x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
-3 + 10x + 12x2 = 0 + 3x2 + -3x2
-3 + 10x + 12x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-3 + 10x + 12x2 = 0

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

Divide each side by '12'.
-0.25 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.8333333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.8333333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.8333333333x + x2 = 0 + 0.25
0.8333333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.8333333333x + x2 = 0.25

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 0.25 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 0.25 + 0.1736111111

Combine like terms: 0.25 + 0.1736111111 = 0.4236111111
0.1736111111 + 0.8333333333x + x2 = 0.4236111111

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.4236111111

Calculate the square root of the right side: 0.65085414

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.65085414 and -0.65085414.

Subproblem 1
x + 0.4166666667 = 0.65085414

Simplifying
x + 0.4166666667 = 0.65085414

Reorder the terms:
0.4166666667 + x = 0.65085414

Solving
0.4166666667 + x = 0.65085414

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 0.65085414 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 0.65085414 + -0.4166666667
x = 0.65085414 + -0.4166666667

Combine like terms: 0.65085414 + -0.4166666667 = 0.2341874733
x = 0.2341874733

Simplifying
x = 0.2341874733

Subproblem 2
x + 0.4166666667 = -0.65085414

Simplifying
x + 0.4166666667 = -0.65085414

Reorder the terms:
0.4166666667 + x = -0.65085414

Solving
0.4166666667 + x = -0.65085414

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -0.65085414 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -0.65085414 + -0.4166666667
x = -0.65085414 + -0.4166666667

Combine like terms: -0.65085414 + -0.4166666667 = -1.0675208067
x = -1.0675208067

Simplifying
x = -1.0675208067

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2341874733, -1.0675208067}