=(x-1)(x-5)

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

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

Reorder the terms:
0 = (-1 + x)(x + -5)

Reorder the terms:
0 = (-1 + x)(-5 + x)

Multiply (-1 + x) * (-5 + x)
0 = (-1(-5 + x) + x(-5 + x))
0 = ((-5 * -1 + x * -1) + x(-5 + x))
0 = ((5 + -1x) + x(-5 + x))
0 = (5 + -1x + (-5 * x + x * x))
0 = (5 + -1x + (-5x + x2))

Combine like terms: -1x + -5x = -6x
0 = (5 + -6x + x2)

Solving
0 = 5 + -6x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-5 + x)(1 + -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 '(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
Solution
x = {5, 1}