2x=(3x-3)(x+4)

Solution for 2x=(3x-3)(x+4) equation:

Simplifying
2x = (3x + -3)(x + 4)

Reorder the terms:
2x = (-3 + 3x)(x + 4)

Reorder the terms:
2x = (-3 + 3x)(4 + x)

Multiply (-3 + 3x) * (4 + x)
2x = (-3(4 + x) + 3x * (4 + x))
2x = ((4 * -3 + x * -3) + 3x * (4 + x))
2x = ((-12 + -3x) + 3x * (4 + x))
2x = (-12 + -3x + (4 * 3x + x * 3x))
2x = (-12 + -3x + (12x + 3x2))

Combine like terms: -3x + 12x = 9x
2x = (-12 + 9x + 3x2)

Solving
2x = -12 + 9x + 3x2

Solving for variable 'x'.

Reorder the terms:
12 + 2x + -9x + -3x2 = -12 + 9x + 3x2 + 12 + -9x + -3x2

Combine like terms: 2x + -9x = -7x
12 + -7x + -3x2 = -12 + 9x + 3x2 + 12 + -9x + -3x2

Reorder the terms:
12 + -7x + -3x2 = -12 + 12 + 9x + -9x + 3x2 + -3x2

Combine like terms: -12 + 12 = 0
12 + -7x + -3x2 = 0 + 9x + -9x + 3x2 + -3x2
12 + -7x + -3x2 = 9x + -9x + 3x2 + -3x2

Combine like terms: 9x + -9x = 0
12 + -7x + -3x2 = 0 + 3x2 + -3x2
12 + -7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + -7x + -3x2 = 0

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

Divide each side by '-3'.
-4 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 2.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2.333333333x + x2 = 0 + 4
2.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
2.333333333x + x2 = 4

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 = 4 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 4 + 1.361111112

Combine like terms: 4 + 1.361111112 = 5.361111112
1.361111112 + 2.333333333x + x2 = 5.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 5.361111112

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 2.315407332 and -2.315407332.

Subproblem 1
x + 1.166666667 = 2.315407332

Simplifying
x + 1.166666667 = 2.315407332

Reorder the terms:
1.166666667 + x = 2.315407332

Solving
1.166666667 + x = 2.315407332

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 = 2.315407332 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 2.315407332 + -1.166666667
x = 2.315407332 + -1.166666667

Combine like terms: 2.315407332 + -1.166666667 = 1.148740665
x = 1.148740665

Simplifying
x = 1.148740665

Subproblem 2
x + 1.166666667 = -2.315407332

Simplifying
x + 1.166666667 = -2.315407332

Reorder the terms:
1.166666667 + x = -2.315407332

Solving
1.166666667 + x = -2.315407332

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 = -2.315407332 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -2.315407332 + -1.166666667
x = -2.315407332 + -1.166666667

Combine like terms: -2.315407332 + -1.166666667 = -3.482073999
x = -3.482073999

Simplifying
x = -3.482073999

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.148740665, -3.482073999}