3(x+4)-2(x-1)=2x(x-5)+2-3x

Solution for 3(x+4)-2(x-1)=2x(x-5)+2-3x equation:

Simplifying
3(x + 4) + -2(x + -1) = 2x(x + -5) + 2 + -3x

Reorder the terms:
3(4 + x) + -2(x + -1) = 2x(x + -5) + 2 + -3x
(4 * 3 + x * 3) + -2(x + -1) = 2x(x + -5) + 2 + -3x
(12 + 3x) + -2(x + -1) = 2x(x + -5) + 2 + -3x

Reorder the terms:
12 + 3x + -2(-1 + x) = 2x(x + -5) + 2 + -3x
12 + 3x + (-1 * -2 + x * -2) = 2x(x + -5) + 2 + -3x
12 + 3x + (2 + -2x) = 2x(x + -5) + 2 + -3x

Reorder the terms:
12 + 2 + 3x + -2x = 2x(x + -5) + 2 + -3x

Combine like terms: 12 + 2 = 14
14 + 3x + -2x = 2x(x + -5) + 2 + -3x

Combine like terms: 3x + -2x = 1x
14 + 1x = 2x(x + -5) + 2 + -3x

Reorder the terms:
14 + 1x = 2x(-5 + x) + 2 + -3x
14 + 1x = (-5 * 2x + x * 2x) + 2 + -3x
14 + 1x = (-10x + 2x2) + 2 + -3x

Reorder the terms:
14 + 1x = 2 + -10x + -3x + 2x2

Combine like terms: -10x + -3x = -13x
14 + 1x = 2 + -13x + 2x2

Solving
14 + 1x = 2 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
14 + -2 + 1x + 13x + -2x2 = 2 + -13x + 2x2 + -2 + 13x + -2x2

Combine like terms: 14 + -2 = 12
12 + 1x + 13x + -2x2 = 2 + -13x + 2x2 + -2 + 13x + -2x2

Combine like terms: 1x + 13x = 14x
12 + 14x + -2x2 = 2 + -13x + 2x2 + -2 + 13x + -2x2

Reorder the terms:
12 + 14x + -2x2 = 2 + -2 + -13x + 13x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
12 + 14x + -2x2 = 0 + -13x + 13x + 2x2 + -2x2
12 + 14x + -2x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
12 + 14x + -2x2 = 0 + 2x2 + -2x2
12 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + 7x + -1x2 = 0

Solving
6 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -7x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7x + x2 = 0 + 6
-7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7x + x2 = 6

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7x + x2 = 18.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + -3.5 = 4.272001873

Simplifying
x + -3.5 = 4.272001873

Reorder the terms:
-3.5 + x = 4.272001873

Solving
-3.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.272001873 + 3.5
x = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
x = 7.772001873

Simplifying
x = 7.772001873

Subproblem 2
x + -3.5 = -4.272001873

Simplifying
x + -3.5 = -4.272001873

Reorder the terms:
-3.5 + x = -4.272001873

Solving
-3.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.272001873 + 3.5
x = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
x = -0.772001873

Simplifying
x = -0.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.772001873, -0.772001873}
Solution
x = {7.772001873, -0.772001873}