(x-5)(x-45)=0

Solution for (x-5)(x-45)=0 equation:

Simplifying
(x + -5)(x + -45) = 0

Reorder the terms:
(-5 + x)(x + -45) = 0

Reorder the terms:
(-5 + x)(-45 + x) = 0

Multiply (-5 + x) * (-45 + x)
(-5(-45 + x) + x(-45 + x)) = 0
((-45 * -5 + x * -5) + x(-45 + x)) = 0
((225 + -5x) + x(-45 + x)) = 0
(225 + -5x + (-45 * x + x * x)) = 0
(225 + -5x + (-45x + x2)) = 0

Combine like terms: -5x + -45x = -50x
(225 + -50x + x2) = 0

Solving
225 + -50x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(45 + -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 '(45 + -1x)' equal to zero and attempt to solve:

Simplifying
45 + -1x = 0

Solving
45 + -1x = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1x = 0 + -45
-1x = 0 + -45

Combine like terms: 0 + -45 = -45
-1x = -45

Divide each side by '-1'.
x = 45

Simplifying
x = 45
Solution
x = {5, 45}