(M-4)x^2-2(m-2)x+m-1=0

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Solution for (M-4)x^2-2(m-2)x+m-1=0 equation: 


Simplifying
(M + -4) * x2 + -2(m + -2) * x + m + -1 = 0

Reorder the terms:
(-4 + M) * x2 + -2(m + -2) * x + m + -1 = 0

Reorder the terms for easier multiplication:
x2(-4 + M) + -2(m + -2) * x + m + -1 = 0
(-4 * x2 + M * x2) + -2(m + -2) * x + m + -1 = 0
(-4x2 + x2M) + -2(m + -2) * x + m + -1 = 0

Reorder the terms:
-4x2 + x2M + -2(-2 + m) * x + m + -1 = 0

Reorder the terms for easier multiplication:
-4x2 + x2M + -2x(-2 + m) + m + -1 = 0
-4x2 + x2M + (-2 * -2x + m * -2x) + m + -1 = 0

Reorder the terms:
-4x2 + x2M + (-2mx + 4x) + m + -1 = 0
-4x2 + x2M + (-2mx + 4x) + m + -1 = 0

Reorder the terms:
-1 + m + -2mx + 4x + -4x2 + x2M = 0

Solving
-1 + m + -2mx + 4x + -4x2 + 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 + 4x + -4x2 + 1 + x2M = 0 + 1

Reorder the terms:
-1 + 1 + m + -2mx + 4x + -4x2 + x2M = 0 + 1

Combine like terms: -1 + 1 = 0
0 + m + -2mx + 4x + -4x2 + x2M = 0 + 1
m + -2mx + 4x + -4x2 + x2M = 0 + 1

Combine like terms: 0 + 1 = 1
m + -2mx + 4x + -4x2 + x2M = 1

Add '-4x' to each side of the equation.
m + -2mx + 4x + -4x2 + -4x + x2M = 1 + -4x

Reorder the terms:
m + -2mx + 4x + -4x + -4x2 + x2M = 1 + -4x

Combine like terms: 4x + -4x = 0
m + -2mx + 0 + -4x2 + x2M = 1 + -4x
m + -2mx + -4x2 + x2M = 1 + -4x

Add '4x2' to each side of the equation.
m + -2mx + -4x2 + 4x2 + x2M = 1 + -4x + 4x2

Combine like terms: -4x2 + 4x2 = 0
m + -2mx + 0 + x2M = 1 + -4x + 4x2
m + -2mx + x2M = 1 + -4x + 4x2

Add '-1x2M' to each side of the equation.
m + -2mx + x2M + -1x2M = 1 + -4x + 4x2 + -1x2M

Combine like terms: x2M + -1x2M = 0
m + -2mx + 0 = 1 + -4x + 4x2 + -1x2M
m + -2mx = 1 + -4x + 4x2 + -1x2M

Reorder the terms:
-1 + m + -2mx + 4x + -4x2 + x2M = 1 + -4x + 4x2 + -1x2M + -1 + 4x + -4x2 + x2M

Reorder the terms:
-1 + m + -2mx + 4x + -4x2 + x2M = 1 + -1 + -4x + 4x + 4x2 + -4x2 + -1x2M + x2M

Combine like terms: 1 + -1 = 0
-1 + m + -2mx + 4x + -4x2 + x2M = 0 + -4x + 4x + 4x2 + -4x2 + -1x2M + x2M
-1 + m + -2mx + 4x + -4x2 + x2M = -4x + 4x + 4x2 + -4x2 + -1x2M + x2M

Combine like terms: -4x + 4x = 0
-1 + m + -2mx + 4x + -4x2 + x2M = 0 + 4x2 + -4x2 + -1x2M + x2M
-1 + m + -2mx + 4x + -4x2 + x2M = 4x2 + -4x2 + -1x2M + x2M

Combine like terms: 4x2 + -4x2 = 0
-1 + m + -2mx + 4x + -4x2 + x2M = 0 + -1x2M + x2M
-1 + m + -2mx + 4x + -4x2 + x2M = -1x2M + x2M

Combine like terms: -1x2M + x2M = 0
-1 + m + -2mx + 4x + -4x2 + x2M = 0

The solution to this equation could not be determined.

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