(M-1)x^2-2mx+m-1=0

Solution for (M-1)x^2-2mx+m-1=0 equation:

Simplifying
(M + -1) * x2 + -2mx + m + -1 = 0

Reorder the terms:
(-1 + M) * x2 + -2mx + m + -1 = 0

Reorder the terms for easier multiplication:
x2(-1 + M) + -2mx + m + -1 = 0
(-1 * x2 + M * x2) + -2mx + m + -1 = 0
(-1x2 + x2M) + -2mx + m + -1 = 0

Reorder the terms:
-1 + m + -2mx + -1x2 + x2M = 0

Solving
-1 + m + -2mx + -1x2 + x2M = 0

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + m + -2mx + -1x2 + 1 + x2M = 0 + 1

Reorder the terms:
-1 + 1 + m + -2mx + -1x2 + x2M = 0 + 1

Combine like terms: -1 + 1 = 0
0 + m + -2mx + -1x2 + x2M = 0 + 1
m + -2mx + -1x2 + x2M = 0 + 1

Combine like terms: 0 + 1 = 1
m + -2mx + -1x2 + x2M = 1

Add 'x2' to each side of the equation.
m + -2mx + -1x2 + x2 + x2M = 1 + x2

Combine like terms: -1x2 + x2 = 0
m + -2mx + 0 + x2M = 1 + x2
m + -2mx + x2M = 1 + x2

Add '-1x2M' to each side of the equation.
m + -2mx + x2M + -1x2M = 1 + x2 + -1x2M

Combine like terms: x2M + -1x2M = 0
m + -2mx + 0 = 1 + x2 + -1x2M
m + -2mx = 1 + x2 + -1x2M

Reorder the terms:
-1 + m + -2mx + -1x2 + x2M = 1 + x2 + -1x2M + -1 + -1x2 + x2M

Reorder the terms:
-1 + m + -2mx + -1x2 + x2M = 1 + -1 + x2 + -1x2 + -1x2M + x2M

Combine like terms: 1 + -1 = 0
-1 + m + -2mx + -1x2 + x2M = 0 + x2 + -1x2 + -1x2M + x2M
-1 + m + -2mx + -1x2 + x2M = x2 + -1x2 + -1x2M + x2M

Combine like terms: x2 + -1x2 = 0
-1 + m + -2mx + -1x2 + x2M = 0 + -1x2M + x2M
-1 + m + -2mx + -1x2 + x2M = -1x2M + x2M

Combine like terms: -1x2M + x2M = 0
-1 + m + -2mx + -1x2 + x2M = 0

The solution to this equation could not be determined.