(a-1)(a-4)x=a-2(x+1)

Solution for (a-1)(a-4)x=a-2(x+1) equation:

Simplifying
(a + -1)(a + -4) * x = a + -2(x + 1)

Reorder the terms:
(-1 + a)(a + -4) * x = a + -2(x + 1)

Reorder the terms:
(-1 + a)(-4 + a) * x = a + -2(x + 1)

Reorder the terms for easier multiplication:
x(-1 + a)(-4 + a) = a + -2(x + 1)

Multiply (-1 + a) * (-4 + a)
x(-1(-4 + a) + a(-4 + a)) = a + -2(x + 1)
x((-4 * -1 + a * -1) + a(-4 + a)) = a + -2(x + 1)
x((4 + -1a) + a(-4 + a)) = a + -2(x + 1)
x(4 + -1a + (-4 * a + a * a)) = a + -2(x + 1)
x(4 + -1a + (-4a + a2)) = a + -2(x + 1)

Combine like terms: -1a + -4a = -5a
x(4 + -5a + a2) = a + -2(x + 1)
(4 * x + -5a * x + a2 * x) = a + -2(x + 1)

Reorder the terms:
(-5ax + a2x + 4x) = a + -2(x + 1)
(-5ax + a2x + 4x) = a + -2(x + 1)

Reorder the terms:
-5ax + a2x + 4x = a + -2(1 + x)
-5ax + a2x + 4x = a + (1 * -2 + x * -2)
-5ax + a2x + 4x = a + (-2 + -2x)

Reorder the terms:
-5ax + a2x + 4x = -2 + a + -2x

Solving
-5ax + a2x + 4x = -2 + a + -2x

Solving for variable 'a'.

Reorder the terms:
2 + -1a + -5ax + a2x + 4x + 2x = -2 + a + -2x + 2 + -1a + 2x

Combine like terms: 4x + 2x = 6x
2 + -1a + -5ax + a2x + 6x = -2 + a + -2x + 2 + -1a + 2x

Reorder the terms:
2 + -1a + -5ax + a2x + 6x = -2 + 2 + a + -1a + -2x + 2x

Combine like terms: -2 + 2 = 0
2 + -1a + -5ax + a2x + 6x = 0 + a + -1a + -2x + 2x
2 + -1a + -5ax + a2x + 6x = a + -1a + -2x + 2x

Combine like terms: a + -1a = 0
2 + -1a + -5ax + a2x + 6x = 0 + -2x + 2x
2 + -1a + -5ax + a2x + 6x = -2x + 2x

Combine like terms: -2x + 2x = 0
2 + -1a + -5ax + a2x + 6x = 0

The solution to this equation could not be determined.