3(x-4)(2x-7)=2(x+5)

Solution for 3(x-4)(2x-7)=2(x+5) equation:

Simplifying
3(x + -4)(2x + -7) = 2(x + 5)

Reorder the terms:
3(-4 + x)(2x + -7) = 2(x + 5)

Reorder the terms:
3(-4 + x)(-7 + 2x) = 2(x + 5)

Multiply (-4 + x) * (-7 + 2x)
3(-4(-7 + 2x) + x(-7 + 2x)) = 2(x + 5)
3((-7 * -4 + 2x * -4) + x(-7 + 2x)) = 2(x + 5)
3((28 + -8x) + x(-7 + 2x)) = 2(x + 5)
3(28 + -8x + (-7 * x + 2x * x)) = 2(x + 5)
3(28 + -8x + (-7x + 2x2)) = 2(x + 5)

Combine like terms: -8x + -7x = -15x
3(28 + -15x + 2x2) = 2(x + 5)
(28 * 3 + -15x * 3 + 2x2 * 3) = 2(x + 5)
(84 + -45x + 6x2) = 2(x + 5)

Reorder the terms:
84 + -45x + 6x2 = 2(5 + x)
84 + -45x + 6x2 = (5 * 2 + x * 2)
84 + -45x + 6x2 = (10 + 2x)

Solving
84 + -45x + 6x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
84 + -10 + -45x + -2x + 6x2 = 10 + 2x + -10 + -2x

Combine like terms: 84 + -10 = 74
74 + -45x + -2x + 6x2 = 10 + 2x + -10 + -2x

Combine like terms: -45x + -2x = -47x
74 + -47x + 6x2 = 10 + 2x + -10 + -2x

Reorder the terms:
74 + -47x + 6x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
74 + -47x + 6x2 = 0 + 2x + -2x
74 + -47x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
74 + -47x + 6x2 = 0

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

Divide each side by '6'.
12.33333333 + -7.833333333x + x2 = 0

Move the constant term to the right:

Add '-12.33333333' to each side of the equation.
12.33333333 + -7.833333333x + -12.33333333 + x2 = 0 + -12.33333333

Reorder the terms:
12.33333333 + -12.33333333 + -7.833333333x + x2 = 0 + -12.33333333

Combine like terms: 12.33333333 + -12.33333333 = 0.00000000
0.00000000 + -7.833333333x + x2 = 0 + -12.33333333
-7.833333333x + x2 = 0 + -12.33333333

Combine like terms: 0 + -12.33333333 = -12.33333333
-7.833333333x + x2 = -12.33333333

The x term is -7.833333333x.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x + 15.34027778 + x2 = -12.33333333 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x + x2 = -12.33333333 + 15.34027778

Combine like terms: -12.33333333 + 15.34027778 = 3.00694445
15.34027778 + -7.833333333x + x2 = 3.00694445

Factor a perfect square on the left side:
(x + -3.916666667)(x + -3.916666667) = 3.00694445

Calculate the square root of the right side: 1.734054339

Break this problem into two subproblems by setting 
(x + -3.916666667) equal to 1.734054339 and -1.734054339.

Subproblem 1
x + -3.916666667 = 1.734054339

Simplifying
x + -3.916666667 = 1.734054339

Reorder the terms:
-3.916666667 + x = 1.734054339

Solving
-3.916666667 + x = 1.734054339

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = 1.734054339 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = 1.734054339 + 3.916666667
x = 1.734054339 + 3.916666667

Combine like terms: 1.734054339 + 3.916666667 = 5.650721006
x = 5.650721006

Simplifying
x = 5.650721006

Subproblem 2
x + -3.916666667 = -1.734054339

Simplifying
x + -3.916666667 = -1.734054339

Reorder the terms:
-3.916666667 + x = -1.734054339

Solving
-3.916666667 + x = -1.734054339

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = -1.734054339 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = -1.734054339 + 3.916666667
x = -1.734054339 + 3.916666667

Combine like terms: -1.734054339 + 3.916666667 = 2.182612328
x = 2.182612328

Simplifying
x = 2.182612328

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.650721006, 2.182612328}