(x-5)(x-50)=0

Solution for (x-5)(x-50)=0 equation:

Simplifying
(x + -5)(x + -50) = 0

Reorder the terms:
(-5 + x)(x + -50) = 0

Reorder the terms:
(-5 + x)(-50 + x) = 0

Multiply (-5 + x) * (-50 + x)
(-5(-50 + x) + x(-50 + x)) = 0
((-50 * -5 + x * -5) + x(-50 + x)) = 0
((250 + -5x) + x(-50 + x)) = 0
(250 + -5x + (-50 * x + x * x)) = 0
(250 + -5x + (-50x + x2)) = 0

Combine like terms: -5x + -50x = -55x
(250 + -55x + x2) = 0

Solving
250 + -55x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(50 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Solution
x = {5, 50}