(4x-3)(x+4)=(x-2)(2-6x)

Solution for (4x-3)(x+4)=(x-2)(2-6x) equation:

Simplifying
(4x + -3)(x + 4) = (x + -2)(2 + -6x)

Reorder the terms:
(-3 + 4x)(x + 4) = (x + -2)(2 + -6x)

Reorder the terms:
(-3 + 4x)(4 + x) = (x + -2)(2 + -6x)

Multiply (-3 + 4x) * (4 + x)
(-3(4 + x) + 4x * (4 + x)) = (x + -2)(2 + -6x)
((4 * -3 + x * -3) + 4x * (4 + x)) = (x + -2)(2 + -6x)
((-12 + -3x) + 4x * (4 + x)) = (x + -2)(2 + -6x)
(-12 + -3x + (4 * 4x + x * 4x)) = (x + -2)(2 + -6x)
(-12 + -3x + (16x + 4x2)) = (x + -2)(2 + -6x)

Combine like terms: -3x + 16x = 13x
(-12 + 13x + 4x2) = (x + -2)(2 + -6x)

Reorder the terms:
-12 + 13x + 4x2 = (-2 + x)(2 + -6x)

Multiply (-2 + x) * (2 + -6x)
-12 + 13x + 4x2 = (-2(2 + -6x) + x(2 + -6x))
-12 + 13x + 4x2 = ((2 * -2 + -6x * -2) + x(2 + -6x))
-12 + 13x + 4x2 = ((-4 + 12x) + x(2 + -6x))
-12 + 13x + 4x2 = (-4 + 12x + (2 * x + -6x * x))
-12 + 13x + 4x2 = (-4 + 12x + (2x + -6x2))

Combine like terms: 12x + 2x = 14x
-12 + 13x + 4x2 = (-4 + 14x + -6x2)

Solving
-12 + 13x + 4x2 = -4 + 14x + -6x2

Solving for variable 'x'.

Reorder the terms:
-12 + 4 + 13x + -14x + 4x2 + 6x2 = -4 + 14x + -6x2 + 4 + -14x + 6x2

Combine like terms: -12 + 4 = -8
-8 + 13x + -14x + 4x2 + 6x2 = -4 + 14x + -6x2 + 4 + -14x + 6x2

Combine like terms: 13x + -14x = -1x
-8 + -1x + 4x2 + 6x2 = -4 + 14x + -6x2 + 4 + -14x + 6x2

Combine like terms: 4x2 + 6x2 = 10x2
-8 + -1x + 10x2 = -4 + 14x + -6x2 + 4 + -14x + 6x2

Reorder the terms:
-8 + -1x + 10x2 = -4 + 4 + 14x + -14x + -6x2 + 6x2

Combine like terms: -4 + 4 = 0
-8 + -1x + 10x2 = 0 + 14x + -14x + -6x2 + 6x2
-8 + -1x + 10x2 = 14x + -14x + -6x2 + 6x2

Combine like terms: 14x + -14x = 0
-8 + -1x + 10x2 = 0 + -6x2 + 6x2
-8 + -1x + 10x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-8 + -1x + 10x2 = 0

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

Divide each side by '10'.
-0.8 + -0.1x + x2 = 0.0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.1x + 0.8 + x2 = 0.0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.1x + x2 = 0.0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.1x + x2 = 0.0 + 0.8
-0.1x + x2 = 0.0 + 0.8

Combine like terms: 0.0 + 0.8 = 0.8
-0.1x + x2 = 0.8

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 0.8 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 0.8 + 0.0025

Combine like terms: 0.8 + 0.0025 = 0.8025
0.0025 + -0.1x + x2 = 0.8025

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 0.8025

Calculate the square root of the right side: 0.895823643

Break this problem into two subproblems by setting 
(x + -0.05) equal to 0.895823643 and -0.895823643.

Subproblem 1
x + -0.05 = 0.895823643

Simplifying
x + -0.05 = 0.895823643

Reorder the terms:
-0.05 + x = 0.895823643

Solving
-0.05 + x = 0.895823643

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = 0.895823643 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = 0.895823643 + 0.05
x = 0.895823643 + 0.05

Combine like terms: 0.895823643 + 0.05 = 0.945823643
x = 0.945823643

Simplifying
x = 0.945823643

Subproblem 2
x + -0.05 = -0.895823643

Simplifying
x + -0.05 = -0.895823643

Reorder the terms:
-0.05 + x = -0.895823643

Solving
-0.05 + x = -0.895823643

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = -0.895823643 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = -0.895823643 + 0.05
x = -0.895823643 + 0.05

Combine like terms: -0.895823643 + 0.05 = -0.845823643
x = -0.845823643

Simplifying
x = -0.845823643

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.945823643, -0.845823643}