(6x-7)(x-2)=(x-3)(7x-6)

Solution for (6x-7)(x-2)=(x-3)(7x-6) equation:

Simplifying
(6x + -7)(x + -2) = (x + -3)(7x + -6)

Reorder the terms:
(-7 + 6x)(x + -2) = (x + -3)(7x + -6)

Reorder the terms:
(-7 + 6x)(-2 + x) = (x + -3)(7x + -6)

Multiply (-7 + 6x) * (-2 + x)
(-7(-2 + x) + 6x * (-2 + x)) = (x + -3)(7x + -6)
((-2 * -7 + x * -7) + 6x * (-2 + x)) = (x + -3)(7x + -6)
((14 + -7x) + 6x * (-2 + x)) = (x + -3)(7x + -6)
(14 + -7x + (-2 * 6x + x * 6x)) = (x + -3)(7x + -6)
(14 + -7x + (-12x + 6x2)) = (x + -3)(7x + -6)

Combine like terms: -7x + -12x = -19x
(14 + -19x + 6x2) = (x + -3)(7x + -6)

Reorder the terms:
14 + -19x + 6x2 = (-3 + x)(7x + -6)

Reorder the terms:
14 + -19x + 6x2 = (-3 + x)(-6 + 7x)

Multiply (-3 + x) * (-6 + 7x)
14 + -19x + 6x2 = (-3(-6 + 7x) + x(-6 + 7x))
14 + -19x + 6x2 = ((-6 * -3 + 7x * -3) + x(-6 + 7x))
14 + -19x + 6x2 = ((18 + -21x) + x(-6 + 7x))
14 + -19x + 6x2 = (18 + -21x + (-6 * x + 7x * x))
14 + -19x + 6x2 = (18 + -21x + (-6x + 7x2))

Combine like terms: -21x + -6x = -27x
14 + -19x + 6x2 = (18 + -27x + 7x2)

Solving
14 + -19x + 6x2 = 18 + -27x + 7x2

Solving for variable 'x'.

Reorder the terms:
14 + -18 + -19x + 27x + 6x2 + -7x2 = 18 + -27x + 7x2 + -18 + 27x + -7x2

Combine like terms: 14 + -18 = -4
-4 + -19x + 27x + 6x2 + -7x2 = 18 + -27x + 7x2 + -18 + 27x + -7x2

Combine like terms: -19x + 27x = 8x
-4 + 8x + 6x2 + -7x2 = 18 + -27x + 7x2 + -18 + 27x + -7x2

Combine like terms: 6x2 + -7x2 = -1x2
-4 + 8x + -1x2 = 18 + -27x + 7x2 + -18 + 27x + -7x2

Reorder the terms:
-4 + 8x + -1x2 = 18 + -18 + -27x + 27x + 7x2 + -7x2

Combine like terms: 18 + -18 = 0
-4 + 8x + -1x2 = 0 + -27x + 27x + 7x2 + -7x2
-4 + 8x + -1x2 = -27x + 27x + 7x2 + -7x2

Combine like terms: -27x + 27x = 0
-4 + 8x + -1x2 = 0 + 7x2 + -7x2
-4 + 8x + -1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-4 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -8x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -8x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8x + x2 = 0 + -4
-8x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8x + x2 = -4

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -4 + 16

Reorder the terms:
16 + -8x + x2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8x + x2 = 12

Factor a perfect square on the left side:
(x + -4)(x + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -4 = 3.464101615

Simplifying
x + -4 = 3.464101615

Reorder the terms:
-4 + x = 3.464101615

Solving
-4 + x = 3.464101615

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.464101615 + 4
x = 3.464101615 + 4

Combine like terms: 3.464101615 + 4 = 7.464101615
x = 7.464101615

Simplifying
x = 7.464101615

Subproblem 2
x + -4 = -3.464101615

Simplifying
x + -4 = -3.464101615

Reorder the terms:
-4 + x = -3.464101615

Solving
-4 + x = -3.464101615

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.464101615 + 4
x = -3.464101615 + 4

Combine like terms: -3.464101615 + 4 = 0.535898385
x = 0.535898385

Simplifying
x = 0.535898385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.464101615, 0.535898385}