(x-6)(x-7)-(3x-8)(x-4)=

Solution for (x-6)(x-7)-(3x-8)(x-4)= equation:

Simplifying
(x + -6)(x + -7) + -1(3x + -8)(x + -4) = 0

Reorder the terms:
(-6 + x)(x + -7) + -1(3x + -8)(x + -4) = 0

Reorder the terms:
(-6 + x)(-7 + x) + -1(3x + -8)(x + -4) = 0

Multiply (-6 + x) * (-7 + x)
(-6(-7 + x) + x(-7 + x)) + -1(3x + -8)(x + -4) = 0
((-7 * -6 + x * -6) + x(-7 + x)) + -1(3x + -8)(x + -4) = 0
((42 + -6x) + x(-7 + x)) + -1(3x + -8)(x + -4) = 0
(42 + -6x + (-7 * x + x * x)) + -1(3x + -8)(x + -4) = 0
(42 + -6x + (-7x + x2)) + -1(3x + -8)(x + -4) = 0

Combine like terms: -6x + -7x = -13x
(42 + -13x + x2) + -1(3x + -8)(x + -4) = 0

Reorder the terms:
42 + -13x + x2 + -1(-8 + 3x)(x + -4) = 0

Reorder the terms:
42 + -13x + x2 + -1(-8 + 3x)(-4 + x) = 0

Multiply (-8 + 3x) * (-4 + x)
42 + -13x + x2 + -1(-8(-4 + x) + 3x * (-4 + x)) = 0
42 + -13x + x2 + -1((-4 * -8 + x * -8) + 3x * (-4 + x)) = 0
42 + -13x + x2 + -1((32 + -8x) + 3x * (-4 + x)) = 0
42 + -13x + x2 + -1(32 + -8x + (-4 * 3x + x * 3x)) = 0
42 + -13x + x2 + -1(32 + -8x + (-12x + 3x2)) = 0

Combine like terms: -8x + -12x = -20x
42 + -13x + x2 + -1(32 + -20x + 3x2) = 0
42 + -13x + x2 + (32 * -1 + -20x * -1 + 3x2 * -1) = 0
42 + -13x + x2 + (-32 + 20x + -3x2) = 0

Reorder the terms:
42 + -32 + -13x + 20x + x2 + -3x2 = 0

Combine like terms: 42 + -32 = 10
10 + -13x + 20x + x2 + -3x2 = 0

Combine like terms: -13x + 20x = 7x
10 + 7x + x2 + -3x2 = 0

Combine like terms: x2 + -3x2 = -2x2
10 + 7x + -2x2 = 0

Solving
10 + 7x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3.5x + x2 = 0 + 5
-3.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3.5x + x2 = 5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + -3.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.839454173 and -2.839454173.

Subproblem 1
x + -1.75 = 2.839454173

Simplifying
x + -1.75 = 2.839454173

Reorder the terms:
-1.75 + x = 2.839454173

Solving
-1.75 + x = 2.839454173

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.839454173 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.839454173 + 1.75
x = 2.839454173 + 1.75

Combine like terms: 2.839454173 + 1.75 = 4.589454173
x = 4.589454173

Simplifying
x = 4.589454173

Subproblem 2
x + -1.75 = -2.839454173

Simplifying
x + -1.75 = -2.839454173

Reorder the terms:
-1.75 + x = -2.839454173

Solving
-1.75 + x = -2.839454173

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.839454173 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.839454173 + 1.75
x = -2.839454173 + 1.75

Combine like terms: -2.839454173 + 1.75 = -1.089454173
x = -1.089454173

Simplifying
x = -1.089454173

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.589454173, -1.089454173}