(3x-8)(x+1)=(x-4)(2-1)

Solution for (3x-8)(x+1)=(x-4)(2-1) equation:

Simplifying
(3x + -8)(x + 1) = (x + -4)(2 + -1)

Reorder the terms:
(-8 + 3x)(x + 1) = (x + -4)(2 + -1)

Reorder the terms:
(-8 + 3x)(1 + x) = (x + -4)(2 + -1)

Multiply (-8 + 3x) * (1 + x)
(-8(1 + x) + 3x * (1 + x)) = (x + -4)(2 + -1)
((1 * -8 + x * -8) + 3x * (1 + x)) = (x + -4)(2 + -1)
((-8 + -8x) + 3x * (1 + x)) = (x + -4)(2 + -1)
(-8 + -8x + (1 * 3x + x * 3x)) = (x + -4)(2 + -1)
(-8 + -8x + (3x + 3x2)) = (x + -4)(2 + -1)

Combine like terms: -8x + 3x = -5x
(-8 + -5x + 3x2) = (x + -4)(2 + -1)

Reorder the terms:
-8 + -5x + 3x2 = (-4 + x)(2 + -1)

Combine like terms: 2 + -1 = 1
-8 + -5x + 3x2 = (-4 + x)(1)

Reorder the terms for easier multiplication:
-8 + -5x + 3x2 = 1(-4 + x)
-8 + -5x + 3x2 = (-4 * 1 + x * 1)
-8 + -5x + 3x2 = (-4 + 1x)

Solving
-8 + -5x + 3x2 = -4 + 1x

Solving for variable 'x'.

Reorder the terms:
-8 + 4 + -5x + -1x + 3x2 = -4 + 1x + 4 + -1x

Combine like terms: -8 + 4 = -4
-4 + -5x + -1x + 3x2 = -4 + 1x + 4 + -1x

Combine like terms: -5x + -1x = -6x
-4 + -6x + 3x2 = -4 + 1x + 4 + -1x

Reorder the terms:
-4 + -6x + 3x2 = -4 + 4 + 1x + -1x

Combine like terms: -4 + 4 = 0
-4 + -6x + 3x2 = 0 + 1x + -1x
-4 + -6x + 3x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
-4 + -6x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -2x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -2x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.333333333
-2x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-2x + x2 = 1.333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.333333333 + 1

Reorder the terms:
1 + -2x + x2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + -2x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -1) equal to 1.527525232 and -1.527525232.

Subproblem 1
x + -1 = 1.527525232

Simplifying
x + -1 = 1.527525232

Reorder the terms:
-1 + x = 1.527525232

Solving
-1 + x = 1.527525232

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.527525232 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.527525232 + 1
x = 1.527525232 + 1

Combine like terms: 1.527525232 + 1 = 2.527525232
x = 2.527525232

Simplifying
x = 2.527525232

Subproblem 2
x + -1 = -1.527525232

Simplifying
x + -1 = -1.527525232

Reorder the terms:
-1 + x = -1.527525232

Solving
-1 + x = -1.527525232

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.527525232 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.527525232 + 1
x = -1.527525232 + 1

Combine like terms: -1.527525232 + 1 = -0.527525232
x = -0.527525232

Simplifying
x = -0.527525232

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.527525232, -0.527525232}