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

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

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

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

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

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

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

Combine like terms: -1x + -10x = -11x
3(5 + -11x + 2x2) = -2(2x + 1)
(5 * 3 + -11x * 3 + 2x2 * 3) = -2(2x + 1)
(15 + -33x + 6x2) = -2(2x + 1)

Reorder the terms:
15 + -33x + 6x2 = -2(1 + 2x)
15 + -33x + 6x2 = (1 * -2 + 2x * -2)
15 + -33x + 6x2 = (-2 + -4x)

Solving
15 + -33x + 6x2 = -2 + -4x

Solving for variable 'x'.

Reorder the terms:
15 + 2 + -33x + 4x + 6x2 = -2 + -4x + 2 + 4x

Combine like terms: 15 + 2 = 17
17 + -33x + 4x + 6x2 = -2 + -4x + 2 + 4x

Combine like terms: -33x + 4x = -29x
17 + -29x + 6x2 = -2 + -4x + 2 + 4x

Reorder the terms:
17 + -29x + 6x2 = -2 + 2 + -4x + 4x

Combine like terms: -2 + 2 = 0
17 + -29x + 6x2 = 0 + -4x + 4x
17 + -29x + 6x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
17 + -29x + 6x2 = 0

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

Divide each side by '6'.
2.833333333 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '-2.833333333' to each side of the equation.
2.833333333 + -4.833333333x + -2.833333333 + x2 = 0 + -2.833333333

Reorder the terms:
2.833333333 + -2.833333333 + -4.833333333x + x2 = 0 + -2.833333333

Combine like terms: 2.833333333 + -2.833333333 = 0.000000000
0.000000000 + -4.833333333x + x2 = 0 + -2.833333333
-4.833333333x + x2 = 0 + -2.833333333

Combine like terms: 0 + -2.833333333 = -2.833333333
-4.833333333x + x2 = -2.833333333

The x term is -4.833333333x.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333x + 5.840277779 + x2 = -2.833333333 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = -2.833333333 + 5.840277779

Combine like terms: -2.833333333 + 5.840277779 = 3.006944446
5.840277779 + -4.833333333x + x2 = 3.006944446

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = 3.006944446

Calculate the square root of the right side: 1.734054338

Break this problem into two subproblems by setting 
(x + -2.416666667) equal to 1.734054338 and -1.734054338.

Subproblem 1
x + -2.416666667 = 1.734054338

Simplifying
x + -2.416666667 = 1.734054338

Reorder the terms:
-2.416666667 + x = 1.734054338

Solving
-2.416666667 + x = 1.734054338

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = 1.734054338 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = 1.734054338 + 2.416666667
x = 1.734054338 + 2.416666667

Combine like terms: 1.734054338 + 2.416666667 = 4.150721005
x = 4.150721005

Simplifying
x = 4.150721005

Subproblem 2
x + -2.416666667 = -1.734054338

Simplifying
x + -2.416666667 = -1.734054338

Reorder the terms:
-2.416666667 + x = -1.734054338

Solving
-2.416666667 + x = -1.734054338

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = -1.734054338 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = -1.734054338 + 2.416666667
x = -1.734054338 + 2.416666667

Combine like terms: -1.734054338 + 2.416666667 = 0.682612329
x = 0.682612329

Simplifying
x = 0.682612329

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.150721005, 0.682612329}