(x-1)(x-5)=-3

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Solution for (x-1)(x-5)=-3 equation: 


Simplifying
(x + -1)(x + -5) = -3

Reorder the terms:
(-1 + x)(x + -5) = -3

Reorder the terms:
(-1 + x)(-5 + x) = -3

Multiply (-1 + x) * (-5 + x)
(-1(-5 + x) + x(-5 + x)) = -3
((-5 * -1 + x * -1) + x(-5 + x)) = -3
((5 + -1x) + x(-5 + x)) = -3
(5 + -1x + (-5 * x + x * x)) = -3
(5 + -1x + (-5x + x2)) = -3

Combine like terms: -1x + -5x = -6x
(5 + -6x + x2) = -3

Solving
5 + -6x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
5 + 3 + -6x + x2 = -3 + 3

Combine like terms: 5 + 3 = 8
8 + -6x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0


Subproblem 1
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

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 = {2, 4}

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