2(3x+4)(x-8)=3(4x+2)-7x+10

Solution for 2(3x+4)(x-8)=3(4x+2)-7x+10 equation:

Simplifying
2(3x + 4)(x + -8) = 3(4x + 2) + -7x + 10

Reorder the terms:
2(4 + 3x)(x + -8) = 3(4x + 2) + -7x + 10

Reorder the terms:
2(4 + 3x)(-8 + x) = 3(4x + 2) + -7x + 10

Multiply (4 + 3x) * (-8 + x)
2(4(-8 + x) + 3x * (-8 + x)) = 3(4x + 2) + -7x + 10
2((-8 * 4 + x * 4) + 3x * (-8 + x)) = 3(4x + 2) + -7x + 10
2((-32 + 4x) + 3x * (-8 + x)) = 3(4x + 2) + -7x + 10
2(-32 + 4x + (-8 * 3x + x * 3x)) = 3(4x + 2) + -7x + 10
2(-32 + 4x + (-24x + 3x2)) = 3(4x + 2) + -7x + 10

Combine like terms: 4x + -24x = -20x
2(-32 + -20x + 3x2) = 3(4x + 2) + -7x + 10
(-32 * 2 + -20x * 2 + 3x2 * 2) = 3(4x + 2) + -7x + 10
(-64 + -40x + 6x2) = 3(4x + 2) + -7x + 10

Reorder the terms:
-64 + -40x + 6x2 = 3(2 + 4x) + -7x + 10
-64 + -40x + 6x2 = (2 * 3 + 4x * 3) + -7x + 10
-64 + -40x + 6x2 = (6 + 12x) + -7x + 10

Reorder the terms:
-64 + -40x + 6x2 = 6 + 10 + 12x + -7x

Combine like terms: 6 + 10 = 16
-64 + -40x + 6x2 = 16 + 12x + -7x

Combine like terms: 12x + -7x = 5x
-64 + -40x + 6x2 = 16 + 5x

Solving
-64 + -40x + 6x2 = 16 + 5x

Solving for variable 'x'.

Reorder the terms:
-64 + -16 + -40x + -5x + 6x2 = 16 + 5x + -16 + -5x

Combine like terms: -64 + -16 = -80
-80 + -40x + -5x + 6x2 = 16 + 5x + -16 + -5x

Combine like terms: -40x + -5x = -45x
-80 + -45x + 6x2 = 16 + 5x + -16 + -5x

Reorder the terms:
-80 + -45x + 6x2 = 16 + -16 + 5x + -5x

Combine like terms: 16 + -16 = 0
-80 + -45x + 6x2 = 0 + 5x + -5x
-80 + -45x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-80 + -45x + 6x2 = 0

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

Divide each side by '6'.
-13.33333333 + -7.5x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -7.5x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -7.5x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -7.5x + x2 = 0 + 13.33333333
-7.5x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-7.5x + x2 = 13.33333333

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 13.33333333 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 13.33333333 + 14.0625

Combine like terms: 13.33333333 + 14.0625 = 27.39583333
14.0625 + -7.5x + x2 = 27.39583333

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 27.39583333

Calculate the square root of the right side: 5.234102915

Break this problem into two subproblems by setting 
(x + -3.75) equal to 5.234102915 and -5.234102915.

Subproblem 1
x + -3.75 = 5.234102915

Simplifying
x + -3.75 = 5.234102915

Reorder the terms:
-3.75 + x = 5.234102915

Solving
-3.75 + x = 5.234102915

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 5.234102915 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 5.234102915 + 3.75
x = 5.234102915 + 3.75

Combine like terms: 5.234102915 + 3.75 = 8.984102915
x = 8.984102915

Simplifying
x = 8.984102915

Subproblem 2
x + -3.75 = -5.234102915

Simplifying
x + -3.75 = -5.234102915

Reorder the terms:
-3.75 + x = -5.234102915

Solving
-3.75 + x = -5.234102915

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -5.234102915 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -5.234102915 + 3.75
x = -5.234102915 + 3.75

Combine like terms: -5.234102915 + 3.75 = -1.484102915
x = -1.484102915

Simplifying
x = -1.484102915

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.984102915, -1.484102915}