(x-1)(x-4)=0

Solution for (x-1)(x-4)=0 equation:

Simplifying
(x + -1)(x + -4) = 0

Reorder the terms:
(-1 + x)(x + -4) = 0

Reorder the terms:
(-1 + x)(-4 + x) = 0

Multiply (-1 + x) * (-4 + x)
(-1(-4 + x) + x(-4 + x)) = 0
((-4 * -1 + x * -1) + x(-4 + x)) = 0
((4 + -1x) + x(-4 + x)) = 0
(4 + -1x + (-4 * x + x * x)) = 0
(4 + -1x + (-4x + x2)) = 0

Combine like terms: -1x + -4x = -5x
(4 + -5x + x2) = 0

Solving
4 + -5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(4 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1, 4}