First, we will distribute the terms:
(5-x)(x+5) = 5x + 25 - x^2 - 5x
x(x+10) = x^2 + 10x
Now, we will add these two expressions together and set them equal to 0:
5x + 25 - x^2 - 5x + x^2 + 10x = 0
5x + 25 - 5x + 10x = 0
25 + 10x = 0
10x = -25
x = -2.5
Therefore, the solution to the equation (5-x)(x+5)+x(x+10) = 0 is x = -2.5.
First, we will distribute the terms:
(5-x)(x+5) = 5x + 25 - x^2 - 5x
x(x+10) = x^2 + 10x
Now, we will add these two expressions together and set them equal to 0:
5x + 25 - x^2 - 5x + x^2 + 10x = 0
5x + 25 - 5x + 10x = 0
25 + 10x = 0
10x = -25
x = -2.5
Therefore, the solution to the equation (5-x)(x+5)+x(x+10) = 0 is x = -2.5.