(x-1)(x-5)=-4

Solution for (x-1)(x-5)=-4 equation:

Simplifying
(x + -1)(x + -5) = -4

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

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

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

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

Solving
5 + -6x + x2 = -4

Solving for variable 'x'.

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

Combine like terms: 5 + 4 = 9
9 + -6x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
9 + -6x + x2 = 0

Factor a trinomial.
(3 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}