x^2-10x=x^2-mx+n-n

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Solution for x^2-10x=x^2-mx+n-n equation: 


Simplifying
x2 + -10x = x2 + -1mx + n + -1n

Reorder the terms:
-10x + x2 = x2 + -1mx + n + -1n

Reorder the terms:
-10x + x2 = -1mx + n + -1n + x2

Combine like terms: n + -1n = 0
-10x + x2 = -1mx + 0 + x2
-10x + x2 = -1mx + x2

Add '-1x2' to each side of the equation.
-10x + x2 + -1x2 = -1mx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10x + 0 = -1mx + x2 + -1x2
-10x = -1mx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10x = -1mx + 0
-10x = -1mx

Solving
-10x = -1mx

Solving for variable 'x'.

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

Add 'mx' to each side of the equation.
mx + -10x = -1mx + mx

Combine like terms: -1mx + mx = 0
mx + -10x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(m + -10) = 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 '(m + -10)' equal to zero and attempt to solve:

Simplifying
m + -10 = 0

Reorder the terms:
-10 + m = 0

Solving
-10 + m = 0

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

Add '10' to each side of the equation.
-10 + 10 + m = 0 + 10

Combine like terms: -10 + 10 = 0
0 + m = 0 + 10
m = 0 + 10

Combine like terms: 0 + 10 = 10
m = 10

Add '-1m' to each side of the equation.
m + -1m = 10 + -1m

Combine like terms: m + -1m = 0
0 = 10 + -1m

Simplifying
0 = 10 + -1m

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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