R(x)=P(x)-Q(x)

Solution for R(x)=P(x)-Q(x) equation:

Simplifying
R(x) = P(x) + -1Q(x)

Multiply R * x
xR = P(x) + -1Q(x)

Multiply P * x
xR = xP + -1Q(x)

Multiply Q * x
xR = xP + -1xQ

Solving
xR = xP + -1xQ

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 + -1xQ

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1P + Q + 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 + Q + R)' equal to zero and attempt to solve:

Simplifying
-1P + Q + R = 0

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

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

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

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

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

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

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

Simplifying
0 = P + -1Q + -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}