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

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

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

Reorder the terms:
3(4 + x) + -4 = 2(x + 4) * x
(4 * 3 + x * 3) + -4 = 2(x + 4) * x
(12 + 3x) + -4 = 2(x + 4) * x

Reorder the terms:
12 + -4 + 3x = 2(x + 4) * x

Combine like terms: 12 + -4 = 8
8 + 3x = 2(x + 4) * x

Reorder the terms:
8 + 3x = 2(4 + x) * x

Reorder the terms for easier multiplication:
8 + 3x = 2x(4 + x)
8 + 3x = (4 * 2x + x * 2x)
8 + 3x = (8x + 2x2)

Solving
8 + 3x = 8x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -8x = -5x
8 + -5x + -2x2 = 8x + 2x2 + -8x + -2x2

Reorder the terms:
8 + -5x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
8 + -5x + -2x2 = 0 + 2x2 + -2x2
8 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4 + 2.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 2.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2.5x + x2 = 0 + 4
2.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
2.5x + x2 = 4

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 4 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + 2.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + 1.25 = 2.358495283

Simplifying
x + 1.25 = 2.358495283

Reorder the terms:
1.25 + x = 2.358495283

Solving
1.25 + x = 2.358495283

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.358495283 + -1.25
x = 2.358495283 + -1.25

Combine like terms: 2.358495283 + -1.25 = 1.108495283
x = 1.108495283

Simplifying
x = 1.108495283

Subproblem 2
x + 1.25 = -2.358495283

Simplifying
x + 1.25 = -2.358495283

Reorder the terms:
1.25 + x = -2.358495283

Solving
1.25 + x = -2.358495283

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.358495283 + -1.25
x = -2.358495283 + -1.25

Combine like terms: -2.358495283 + -1.25 = -3.608495283
x = -3.608495283

Simplifying
x = -3.608495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.108495283, -3.608495283}