(x-5)(x-3)=15

Solution for (x-5)(x-3)=15 equation:

Simplifying
(x + -5)(x + -3) = 15

Reorder the terms:
(-5 + x)(x + -3) = 15

Reorder the terms:
(-5 + x)(-3 + x) = 15

Multiply (-5 + x) * (-3 + x)
(-5(-3 + x) + x(-3 + x)) = 15
((-3 * -5 + x * -5) + x(-3 + x)) = 15
((15 + -5x) + x(-3 + x)) = 15
(15 + -5x + (-3 * x + x * x)) = 15
(15 + -5x + (-3x + x2)) = 15

Combine like terms: -5x + -3x = -8x
(15 + -8x + x2) = 15

Add '-15' to each side of the equation.
15 + -8x + -15 + x2 = 15 + -15

Reorder the terms:
15 + -15 + -8x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
0 + -8x + x2 = 15 + -15
-8x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-8x + x2 = 0

Solving
-8x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}