R(x)=P(x)+(Qx)

Solution for R(x)=P(x)+(Qx) equation:

Simplifying
R(x) = P(x) + (Qx)

Multiply R * x
xR = P(x) + (Qx)

Multiply P * x
xR = xP + (Qx)
xR = xP + xQ

Solving
xR = xP + xQ

Solving for variable 'x'.

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

Add '-1xP' to each side of the equation.
-1xP + xR = xP + -1xP + xQ

Combine like terms: xP + -1xP = 0
-1xP + xR = 0 + xQ
-1xP + xR = xQ

Add '-1xQ' to each side of the equation.
-1xP + -1xQ + xR = xQ + -1xQ

Combine like terms: xQ + -1xQ = 0
-1xP + -1xQ + xR = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1P + -1Q + R) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1P + -1Q + R)' equal to zero and attempt to solve:

Simplifying
-1P + -1Q + R = 0

Solving
-1P + -1Q + R = 0

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

Add 'P' to each side of the equation.
-1P + -1Q + P + R = 0 + P

Reorder the terms:
-1P + P + -1Q + R = 0 + P

Combine like terms: -1P + P = 0
0 + -1Q + R = 0 + P
-1Q + R = 0 + P
Remove the zero:
-1Q + R = P

Add 'Q' to each side of the equation.
-1Q + Q + R = P + Q

Combine like terms: -1Q + Q = 0
0 + R = P + Q
R = P + Q

Add '-1R' to each side of the equation.
R + -1R = P + Q + -1R

Combine like terms: R + -1R = 0
0 = P + Q + -1R

Simplifying
0 = P + Q + -1R

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}