4(4x-3)+x(2x-3)=(6x+8)(x-1)

Solution for 4(4x-3)+x(2x-3)=(6x+8)(x-1) equation:

Simplifying
4(4x + -3) + x(2x + -3) = (6x + 8)(x + -1)

Reorder the terms:
4(-3 + 4x) + x(2x + -3) = (6x + 8)(x + -1)
(-3 * 4 + 4x * 4) + x(2x + -3) = (6x + 8)(x + -1)
(-12 + 16x) + x(2x + -3) = (6x + 8)(x + -1)

Reorder the terms:
-12 + 16x + x(-3 + 2x) = (6x + 8)(x + -1)
-12 + 16x + (-3 * x + 2x * x) = (6x + 8)(x + -1)
-12 + 16x + (-3x + 2x2) = (6x + 8)(x + -1)

Combine like terms: 16x + -3x = 13x
-12 + 13x + 2x2 = (6x + 8)(x + -1)

Reorder the terms:
-12 + 13x + 2x2 = (8 + 6x)(x + -1)

Reorder the terms:
-12 + 13x + 2x2 = (8 + 6x)(-1 + x)

Multiply (8 + 6x) * (-1 + x)
-12 + 13x + 2x2 = (8(-1 + x) + 6x * (-1 + x))
-12 + 13x + 2x2 = ((-1 * 8 + x * 8) + 6x * (-1 + x))
-12 + 13x + 2x2 = ((-8 + 8x) + 6x * (-1 + x))
-12 + 13x + 2x2 = (-8 + 8x + (-1 * 6x + x * 6x))
-12 + 13x + 2x2 = (-8 + 8x + (-6x + 6x2))

Combine like terms: 8x + -6x = 2x
-12 + 13x + 2x2 = (-8 + 2x + 6x2)

Solving
-12 + 13x + 2x2 = -8 + 2x + 6x2

Solving for variable 'x'.

Reorder the terms:
-12 + 8 + 13x + -2x + 2x2 + -6x2 = -8 + 2x + 6x2 + 8 + -2x + -6x2

Combine like terms: -12 + 8 = -4
-4 + 13x + -2x + 2x2 + -6x2 = -8 + 2x + 6x2 + 8 + -2x + -6x2

Combine like terms: 13x + -2x = 11x
-4 + 11x + 2x2 + -6x2 = -8 + 2x + 6x2 + 8 + -2x + -6x2

Combine like terms: 2x2 + -6x2 = -4x2
-4 + 11x + -4x2 = -8 + 2x + 6x2 + 8 + -2x + -6x2

Reorder the terms:
-4 + 11x + -4x2 = -8 + 8 + 2x + -2x + 6x2 + -6x2

Combine like terms: -8 + 8 = 0
-4 + 11x + -4x2 = 0 + 2x + -2x + 6x2 + -6x2
-4 + 11x + -4x2 = 2x + -2x + 6x2 + -6x2

Combine like terms: 2x + -2x = 0
-4 + 11x + -4x2 = 0 + 6x2 + -6x2
-4 + 11x + -4x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-4 + 11x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1 + -2.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.75x + x2 = 0 + -1
-2.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.75x + x2 = -1

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = -1 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = -1 + 1.890625

Combine like terms: -1 + 1.890625 = 0.890625
1.890625 + -2.75x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -1.375) equal to 0.943729304 and -0.943729304.

Subproblem 1
x + -1.375 = 0.943729304

Simplifying
x + -1.375 = 0.943729304

Reorder the terms:
-1.375 + x = 0.943729304

Solving
-1.375 + x = 0.943729304

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = 0.943729304 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = 0.943729304 + 1.375
x = 0.943729304 + 1.375

Combine like terms: 0.943729304 + 1.375 = 2.318729304
x = 2.318729304

Simplifying
x = 2.318729304

Subproblem 2
x + -1.375 = -0.943729304

Simplifying
x + -1.375 = -0.943729304

Reorder the terms:
-1.375 + x = -0.943729304

Solving
-1.375 + x = -0.943729304

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = -0.943729304 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = -0.943729304 + 1.375
x = -0.943729304 + 1.375

Combine like terms: -0.943729304 + 1.375 = 0.431270696
x = 0.431270696

Simplifying
x = 0.431270696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.318729304, 0.431270696}