(x-3)(x-1)=15

Solution for (x-3)(x-1)=15 equation:

Simplifying
(x + -3)(x + -1) = 15

Reorder the terms:
(-3 + x)(x + -1) = 15

Reorder the terms:
(-3 + x)(-1 + x) = 15

Multiply (-3 + x) * (-1 + x)
(-3(-1 + x) + x(-1 + x)) = 15
((-1 * -3 + x * -3) + x(-1 + x)) = 15
((3 + -3x) + x(-1 + x)) = 15
(3 + -3x + (-1 * x + x * x)) = 15
(3 + -3x + (-1x + x2)) = 15

Combine like terms: -3x + -1x = -4x
(3 + -4x + x2) = 15

Solving
3 + -4x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
3 + -15 + -4x + x2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + -4x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}