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

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


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

Reorder the terms:
(3 + 4x)(8 + -3x) = 2x(6x + -2)

Multiply (3 + 4x) * (8 + -3x)
(3(8 + -3x) + 4x * (8 + -3x)) = 2x(6x + -2)
((8 * 3 + -3x * 3) + 4x * (8 + -3x)) = 2x(6x + -2)
((24 + -9x) + 4x * (8 + -3x)) = 2x(6x + -2)
(24 + -9x + (8 * 4x + -3x * 4x)) = 2x(6x + -2)
(24 + -9x + (32x + -12x2)) = 2x(6x + -2)

Combine like terms: -9x + 32x = 23x
(24 + 23x + -12x2) = 2x(6x + -2)

Reorder the terms:
24 + 23x + -12x2 = 2x(-2 + 6x)
24 + 23x + -12x2 = (-2 * 2x + 6x * 2x)
24 + 23x + -12x2 = (-4x + 12x2)

Solving
24 + 23x + -12x2 = -4x + 12x2

Solving for variable 'x'.

Reorder the terms:
24 + 23x + 4x + -12x2 + -12x2 = -4x + 12x2 + 4x + -12x2

Combine like terms: 23x + 4x = 27x
24 + 27x + -12x2 + -12x2 = -4x + 12x2 + 4x + -12x2

Combine like terms: -12x2 + -12x2 = -24x2
24 + 27x + -24x2 = -4x + 12x2 + 4x + -12x2

Reorder the terms:
24 + 27x + -24x2 = -4x + 4x + 12x2 + -12x2

Combine like terms: -4x + 4x = 0
24 + 27x + -24x2 = 0 + 12x2 + -12x2
24 + 27x + -24x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
24 + 27x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 9x + -8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 9x + -8x2)' equal to zero and attempt to solve:

Simplifying
8 + 9x + -8x2 = 0

Solving
8 + 9x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1 + -1.125x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.125x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.125x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.125x + x2 = 0 + 1
-1.125x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.125x + x2 = 1

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = 1 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = 1 + 0.31640625

Combine like terms: 1 + 0.31640625 = 1.31640625
0.31640625 + -1.125x + x2 = 1.31640625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 1.31640625

Calculate the square root of the right side: 1.147347484

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 1.147347484 and -1.147347484.


Subproblem 1
x + -0.5625 = 1.147347484

Simplifying
x + -0.5625 = 1.147347484

Reorder the terms:
-0.5625 + x = 1.147347484

Solving
-0.5625 + x = 1.147347484

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = 1.147347484 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = 1.147347484 + 0.5625
x = 1.147347484 + 0.5625

Combine like terms: 1.147347484 + 0.5625 = 1.709847484
x = 1.709847484

Simplifying
x = 1.709847484


Subproblem 2
x + -0.5625 = -1.147347484

Simplifying
x + -0.5625 = -1.147347484

Reorder the terms:
-0.5625 + x = -1.147347484

Solving
-0.5625 + x = -1.147347484

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = -1.147347484 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = -1.147347484 + 0.5625
x = -1.147347484 + 0.5625

Combine like terms: -1.147347484 + 0.5625 = -0.584847484
x = -0.584847484

Simplifying
x = -0.584847484


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.709847484, -0.584847484}
Solution
x = {1.709847484, -0.584847484}

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