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

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

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

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

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

Multiply (-3 + 7x) * (-2 + x)
(-3(-2 + x) + 7x * (-2 + x)) + -4x = 5(3x + -2)
((-2 * -3 + x * -3) + 7x * (-2 + x)) + -4x = 5(3x + -2)
((6 + -3x) + 7x * (-2 + x)) + -4x = 5(3x + -2)
(6 + -3x + (-2 * 7x + x * 7x)) + -4x = 5(3x + -2)
(6 + -3x + (-14x + 7x2)) + -4x = 5(3x + -2)

Combine like terms: -3x + -14x = -17x
(6 + -17x + 7x2) + -4x = 5(3x + -2)

Reorder the terms:
6 + -17x + -4x + 7x2 = 5(3x + -2)

Combine like terms: -17x + -4x = -21x
6 + -21x + 7x2 = 5(3x + -2)

Reorder the terms:
6 + -21x + 7x2 = 5(-2 + 3x)
6 + -21x + 7x2 = (-2 * 5 + 3x * 5)
6 + -21x + 7x2 = (-10 + 15x)

Solving
6 + -21x + 7x2 = -10 + 15x

Solving for variable 'x'.

Reorder the terms:
6 + 10 + -21x + -15x + 7x2 = -10 + 15x + 10 + -15x

Combine like terms: 6 + 10 = 16
16 + -21x + -15x + 7x2 = -10 + 15x + 10 + -15x

Combine like terms: -21x + -15x = -36x
16 + -36x + 7x2 = -10 + 15x + 10 + -15x

Reorder the terms:
16 + -36x + 7x2 = -10 + 10 + 15x + -15x

Combine like terms: -10 + 10 = 0
16 + -36x + 7x2 = 0 + 15x + -15x
16 + -36x + 7x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
16 + -36x + 7x2 = 0

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

Divide each side by '7'.
2.285714286 + -5.142857143x + x2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + -5.142857143x + -2.285714286 + x2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + -5.142857143x + x2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + -5.142857143x + x2 = 0 + -2.285714286
-5.142857143x + x2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
-5.142857143x + x2 = -2.285714286

The x term is -5.142857143x.  Take half its coefficient (-2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
-5.142857143x + 6.612244901 + x2 = -2.285714286 + 6.612244901

Reorder the terms:
6.612244901 + -5.142857143x + x2 = -2.285714286 + 6.612244901

Combine like terms: -2.285714286 + 6.612244901 = 4.326530615
6.612244901 + -5.142857143x + x2 = 4.326530615

Factor a perfect square on the left side:
(x + -2.571428572)(x + -2.571428572) = 4.326530615

Calculate the square root of the right side: 2.080031398

Break this problem into two subproblems by setting 
(x + -2.571428572) equal to 2.080031398 and -2.080031398.

Subproblem 1
x + -2.571428572 = 2.080031398

Simplifying
x + -2.571428572 = 2.080031398

Reorder the terms:
-2.571428572 + x = 2.080031398

Solving
-2.571428572 + x = 2.080031398

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = 2.080031398 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = 2.080031398 + 2.571428572
x = 2.080031398 + 2.571428572

Combine like terms: 2.080031398 + 2.571428572 = 4.65145997
x = 4.65145997

Simplifying
x = 4.65145997

Subproblem 2
x + -2.571428572 = -2.080031398

Simplifying
x + -2.571428572 = -2.080031398

Reorder the terms:
-2.571428572 + x = -2.080031398

Solving
-2.571428572 + x = -2.080031398

Solving for variable 'x'.

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

Add '2.571428572' to each side of the equation.
-2.571428572 + 2.571428572 + x = -2.080031398 + 2.571428572

Combine like terms: -2.571428572 + 2.571428572 = 0.000000000
0.000000000 + x = -2.080031398 + 2.571428572
x = -2.080031398 + 2.571428572

Combine like terms: -2.080031398 + 2.571428572 = 0.491397174
x = 0.491397174

Simplifying
x = 0.491397174

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.65145997, 0.491397174}