P(x)=R(x)-C(x)

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


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

Multiply P * x
xP = R(x) + -1C(x)

Multiply R * x
xP = xR + -1C(x)

Multiply C * x
xP = xR + -1xC

Reorder the terms:
xP = -1xC + xR

Solving
xP = -1xC + xR

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
C + P + -1R = 0

Solving
C + P + -1R = 0

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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

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