Px-37=Qx-37

Solution for Px-37=Qx-37 equation:

Simplifying
Px + -37 = Qx + -37

Reorder the terms:
-37 + xP = Qx + -37

Reorder the terms:
-37 + xP = -37 + xQ

Add '37' to each side of the equation.
-37 + 37 + xP = -37 + 37 + xQ

Combine like terms: -37 + 37 = 0
0 + xP = -37 + 37 + xQ
xP = -37 + 37 + xQ

Combine like terms: -37 + 37 = 0
xP = 0 + xQ
xP = xQ

Solving
xP = xQ

Solving for variable 'x'.

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

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

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

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

Simplifying
P + -1Q = 0

Solving
P + -1Q = 0

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

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

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

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

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

Simplifying
0 = -1P + Q

The solution to this equation could not be determined.

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