3(4x-5)(-2x+3)=2(x-4)

Solution for 3(4x-5)(-2x+3)=2(x-4) equation:

Simplifying
3(4x + -5)(-2x + 3) = 2(x + -4)

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

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

Multiply (-5 + 4x) * (3 + -2x)
3(-5(3 + -2x) + 4x * (3 + -2x)) = 2(x + -4)
3((3 * -5 + -2x * -5) + 4x * (3 + -2x)) = 2(x + -4)
3((-15 + 10x) + 4x * (3 + -2x)) = 2(x + -4)
3(-15 + 10x + (3 * 4x + -2x * 4x)) = 2(x + -4)
3(-15 + 10x + (12x + -8x2)) = 2(x + -4)

Combine like terms: 10x + 12x = 22x
3(-15 + 22x + -8x2) = 2(x + -4)
(-15 * 3 + 22x * 3 + -8x2 * 3) = 2(x + -4)
(-45 + 66x + -24x2) = 2(x + -4)

Reorder the terms:
-45 + 66x + -24x2 = 2(-4 + x)
-45 + 66x + -24x2 = (-4 * 2 + x * 2)
-45 + 66x + -24x2 = (-8 + 2x)

Solving
-45 + 66x + -24x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
-45 + 8 + 66x + -2x + -24x2 = -8 + 2x + 8 + -2x

Combine like terms: -45 + 8 = -37
-37 + 66x + -2x + -24x2 = -8 + 2x + 8 + -2x

Combine like terms: 66x + -2x = 64x
-37 + 64x + -24x2 = -8 + 2x + 8 + -2x

Reorder the terms:
-37 + 64x + -24x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
-37 + 64x + -24x2 = 0 + 2x + -2x
-37 + 64x + -24x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-37 + 64x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
1.541666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.541666667' to each side of the equation.
1.541666667 + -2.666666667x + -1.541666667 + x2 = 0 + -1.541666667

Reorder the terms:
1.541666667 + -1.541666667 + -2.666666667x + x2 = 0 + -1.541666667

Combine like terms: 1.541666667 + -1.541666667 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -1.541666667
-2.666666667x + x2 = 0 + -1.541666667

Combine like terms: 0 + -1.541666667 = -1.541666667
-2.666666667x + x2 = -1.541666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -1.541666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -1.541666667 + 1.777777780

Combine like terms: -1.541666667 + 1.777777780 = 0.236111113
1.777777780 + -2.666666667x + x2 = 0.236111113

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 0.236111113

Calculate the square root of the right side: 0.48591266

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 0.48591266 and -0.48591266.

Subproblem 1
x + -1.333333334 = 0.48591266

Simplifying
x + -1.333333334 = 0.48591266

Reorder the terms:
-1.333333334 + x = 0.48591266

Solving
-1.333333334 + x = 0.48591266

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 0.48591266 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 0.48591266 + 1.333333334
x = 0.48591266 + 1.333333334

Combine like terms: 0.48591266 + 1.333333334 = 1.819245994
x = 1.819245994

Simplifying
x = 1.819245994

Subproblem 2
x + -1.333333334 = -0.48591266

Simplifying
x + -1.333333334 = -0.48591266

Reorder the terms:
-1.333333334 + x = -0.48591266

Solving
-1.333333334 + x = -0.48591266

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -0.48591266 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -0.48591266 + 1.333333334
x = -0.48591266 + 1.333333334

Combine like terms: -0.48591266 + 1.333333334 = 0.847420674
x = 0.847420674

Simplifying
x = 0.847420674

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.819245994, 0.847420674}