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

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

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

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

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

Multiply (-2 + 3x) * (-7 + x)
(-2(-7 + x) + 3x * (-7 + x)) = (x + 2)(2x + -3)
((-7 * -2 + x * -2) + 3x * (-7 + x)) = (x + 2)(2x + -3)
((14 + -2x) + 3x * (-7 + x)) = (x + 2)(2x + -3)
(14 + -2x + (-7 * 3x + x * 3x)) = (x + 2)(2x + -3)
(14 + -2x + (-21x + 3x2)) = (x + 2)(2x + -3)

Combine like terms: -2x + -21x = -23x
(14 + -23x + 3x2) = (x + 2)(2x + -3)

Reorder the terms:
14 + -23x + 3x2 = (2 + x)(2x + -3)

Reorder the terms:
14 + -23x + 3x2 = (2 + x)(-3 + 2x)

Multiply (2 + x) * (-3 + 2x)
14 + -23x + 3x2 = (2(-3 + 2x) + x(-3 + 2x))
14 + -23x + 3x2 = ((-3 * 2 + 2x * 2) + x(-3 + 2x))
14 + -23x + 3x2 = ((-6 + 4x) + x(-3 + 2x))
14 + -23x + 3x2 = (-6 + 4x + (-3 * x + 2x * x))
14 + -23x + 3x2 = (-6 + 4x + (-3x + 2x2))

Combine like terms: 4x + -3x = 1x
14 + -23x + 3x2 = (-6 + 1x + 2x2)

Solving
14 + -23x + 3x2 = -6 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
14 + 6 + -23x + -1x + 3x2 + -2x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Combine like terms: 14 + 6 = 20
20 + -23x + -1x + 3x2 + -2x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Combine like terms: -23x + -1x = -24x
20 + -24x + 3x2 + -2x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
20 + -24x + 1x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Reorder the terms:
20 + -24x + 1x2 = -6 + 6 + 1x + -1x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
20 + -24x + 1x2 = 0 + 1x + -1x + 2x2 + -2x2
20 + -24x + 1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
20 + -24x + 1x2 = 0 + 2x2 + -2x2
20 + -24x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + -24x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -24x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -24x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -24x + x2 = 0 + -20
-24x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-24x + x2 = -20

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -20 + 144

Reorder the terms:
144 + -24x + x2 = -20 + 144

Combine like terms: -20 + 144 = 124
144 + -24x + x2 = 124

Factor a perfect square on the left side:
(x + -12)(x + -12) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + -12) equal to 11.135528726 and -11.135528726.

Subproblem 1
x + -12 = 11.135528726

Simplifying
x + -12 = 11.135528726

Reorder the terms:
-12 + x = 11.135528726

Solving
-12 + x = 11.135528726

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 11.135528726 + 12

Combine like terms: -12 + 12 = 0
0 + x = 11.135528726 + 12
x = 11.135528726 + 12

Combine like terms: 11.135528726 + 12 = 23.135528726
x = 23.135528726

Simplifying
x = 23.135528726

Subproblem 2
x + -12 = -11.135528726

Simplifying
x + -12 = -11.135528726

Reorder the terms:
-12 + x = -11.135528726

Solving
-12 + x = -11.135528726

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -11.135528726 + 12

Combine like terms: -12 + 12 = 0
0 + x = -11.135528726 + 12
x = -11.135528726 + 12

Combine like terms: -11.135528726 + 12 = 0.864471274
x = 0.864471274

Simplifying
x = 0.864471274

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.135528726, 0.864471274}