For which values of p and q does the following equation have infinitely many solutions ? −90x+q=px+45

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     -90*x+q-(p*x+45)=0 

 1.1     Pull out like factors :

   -90x + q - xp - 45  = 

  -1 • (xp + 90x - q + 45) 

 2.1     Solve   -xp-90x+q-45  = 0 

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: