2x(x-5)-(x-5)=0

Factor x-5 out of 2x(x-5).

(x-5)(2x)-(x-5)=0

Factor x-5 out of -(x-5).

(x-5)(2x)+(x-5)⋅-1=0

Factor x-5 out of (x-5)(2x)+(x-5)⋅-1.

(x-5)(2x-1)=0

(x-5)(2x-1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-5=0

2x-1=0

Set the first factor equal to 0.

x-5=0

Add 5 to both sides of the equation.

x=5

x=5

Set the next factor equal to 0.

2x-1=0

Add 1 to both sides of the equation.

2x=1

Divide each term by 2 and simplify.

Divide each term in 2x=1 by 2.

2×2=12

Cancel the common factor of 2.

Cancel the common factor.

2×2=12

Divide x by 1.

x=12

x=12

x=12

x=12

The final solution is all the values that make (x-5)(2x-1)=0 true.

x=5,12

Solve Using the Square Root Property 2x(x-5)-(x-5)=0