x(x-3)(x-2)-6=(x^2-1)(x-4)

Solution for x(x-3)(x-2)-6=(x^2-1)(x-4) equation:

Simplifying
x(x + -3)(x + -2) + -6 = (x2 + -1)(x + -4)

Reorder the terms:
x(-3 + x)(x + -2) + -6 = (x2 + -1)(x + -4)

Reorder the terms:
x(-3 + x)(-2 + x) + -6 = (x2 + -1)(x + -4)

Multiply (-3 + x) * (-2 + x)
x(-3(-2 + x) + x(-2 + x)) + -6 = (x2 + -1)(x + -4)
x((-2 * -3 + x * -3) + x(-2 + x)) + -6 = (x2 + -1)(x + -4)
x((6 + -3x) + x(-2 + x)) + -6 = (x2 + -1)(x + -4)
x(6 + -3x + (-2 * x + x * x)) + -6 = (x2 + -1)(x + -4)
x(6 + -3x + (-2x + x2)) + -6 = (x2 + -1)(x + -4)

Combine like terms: -3x + -2x = -5x
x(6 + -5x + x2) + -6 = (x2 + -1)(x + -4)
(6 * x + -5x * x + x2 * x) + -6 = (x2 + -1)(x + -4)
(6x + -5x2 + x3) + -6 = (x2 + -1)(x + -4)

Reorder the terms:
-6 + 6x + -5x2 + x3 = (x2 + -1)(x + -4)

Reorder the terms:
-6 + 6x + -5x2 + x3 = (-1 + x2)(x + -4)

Reorder the terms:
-6 + 6x + -5x2 + x3 = (-1 + x2)(-4 + x)

Multiply (-1 + x2) * (-4 + x)
-6 + 6x + -5x2 + x3 = (-1(-4 + x) + x2(-4 + x))
-6 + 6x + -5x2 + x3 = ((-4 * -1 + x * -1) + x2(-4 + x))
-6 + 6x + -5x2 + x3 = ((4 + -1x) + x2(-4 + x))
-6 + 6x + -5x2 + x3 = (4 + -1x + (-4 * x2 + x * x2))
-6 + 6x + -5x2 + x3 = (4 + -1x + (-4x2 + x3))
-6 + 6x + -5x2 + x3 = (4 + -1x + -4x2 + x3)

Add '-1x3' to each side of the equation.
-6 + 6x + -5x2 + x3 + -1x3 = 4 + -1x + -4x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-6 + 6x + -5x2 + 0 = 4 + -1x + -4x2 + x3 + -1x3
-6 + 6x + -5x2 = 4 + -1x + -4x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-6 + 6x + -5x2 = 4 + -1x + -4x2 + 0
-6 + 6x + -5x2 = 4 + -1x + -4x2

Solving
-6 + 6x + -5x2 = 4 + -1x + -4x2

Solving for variable 'x'.

Reorder the terms:
-6 + -4 + 6x + x + -5x2 + 4x2 = 4 + -1x + -4x2 + -4 + x + 4x2

Combine like terms: -6 + -4 = -10
-10 + 6x + x + -5x2 + 4x2 = 4 + -1x + -4x2 + -4 + x + 4x2

Combine like terms: 6x + x = 7x
-10 + 7x + -5x2 + 4x2 = 4 + -1x + -4x2 + -4 + x + 4x2

Combine like terms: -5x2 + 4x2 = -1x2
-10 + 7x + -1x2 = 4 + -1x + -4x2 + -4 + x + 4x2

Reorder the terms:
-10 + 7x + -1x2 = 4 + -4 + -1x + x + -4x2 + 4x2

Combine like terms: 4 + -4 = 0
-10 + 7x + -1x2 = 0 + -1x + x + -4x2 + 4x2
-10 + 7x + -1x2 = -1x + x + -4x2 + 4x2

Combine like terms: -1x + x = 0
-10 + 7x + -1x2 = 0 + -4x2 + 4x2
-10 + 7x + -1x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-10 + 7x + -1x2 = 0

Factor a trinomial.
(-5 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {5, 2}