(5x-5)(5-x)=0

Solution for (5x-5)(5-x)=0 equation:

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

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

Multiply (-5 + 5x) * (5 + -1x)
(-5(5 + -1x) + 5x * (5 + -1x)) = 0
((5 * -5 + -1x * -5) + 5x * (5 + -1x)) = 0
((-25 + 5x) + 5x * (5 + -1x)) = 0
(-25 + 5x + (5 * 5x + -1x * 5x)) = 0
(-25 + 5x + (25x + -5x2)) = 0

Combine like terms: 5x + 25x = 30x
(-25 + 30x + -5x2) = 0

Solving
-25 + 30x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 6x + -1x2) = 0

Factor a trinomial.
5((-5 + x)(1 + -1x)) = 0

Ignore the factor 5.
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}