Which values of P and Q does the following equation have infinitely many solutions

Qx-10=-10x+P

that is when you get an identity such as 1=1 or x=x

we must make the coefients of each nth power term the same on both sides

on left side:

Qx-10

Qx is the linear (1st degree) term, its coefient is Q and the variable is x

-10 is the constant (0 degree) term

on right side:

-10x+P

-10x is the linear term (1st degree), its coefient is - 10 and x is the variable

P is the constant term

we need to match constant and linear terms on both sides so they cancel

so set linear terms equal to each other

Qx=-10x

divide both sides by x

Q=-10

now solve for constant terms

-10 and P

set equal to each other

-10=P

easy

so for the values Q=-10 and P=-10 will the equation will have infinitely many solutions