(X-2m+1)(-x+4m+1)=0

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


Simplifying
(X + -2m + 1)(-1x + 4m + 1) = 0

Reorder the terms:
(1 + X + -2m)(-1x + 4m + 1) = 0

Reorder the terms:
(1 + X + -2m)(1 + 4m + -1x) = 0

Multiply (1 + X + -2m) * (1 + 4m + -1x)
(1(1 + 4m + -1x) + X(1 + 4m + -1x) + -2m * (1 + 4m + -1x)) = 0
((1 * 1 + 4m * 1 + -1x * 1) + X(1 + 4m + -1x) + -2m * (1 + 4m + -1x)) = 0
((1 + 4m + -1x) + X(1 + 4m + -1x) + -2m * (1 + 4m + -1x)) = 0
(1 + 4m + -1x + (1 * X + 4m * X + -1x * X) + -2m * (1 + 4m + -1x)) = 0
(1 + 4m + -1x + (1X + 4mX + -1xX) + -2m * (1 + 4m + -1x)) = 0
(1 + 4m + -1x + 1X + 4mX + -1xX + (1 * -2m + 4m * -2m + -1x * -2m)) = 0

Reorder the terms:
(1 + 4m + -1x + 1X + 4mX + -1xX + (-2m + 2mx + -8m2)) = 0
(1 + 4m + -1x + 1X + 4mX + -1xX + (-2m + 2mx + -8m2)) = 0

Reorder the terms:
(1 + 1X + 4m + -2m + 4mX + 2mx + -8m2 + -1x + -1xX) = 0

Combine like terms: 4m + -2m = 2m
(1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX) = 0

Solving
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0

Solving for variable 'X'.

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

Add '-1' to each side of the equation.
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1 + -1xX = 0 + -1

Reorder the terms:
1 + -1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + -1
1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + -1

Combine like terms: 0 + -1 = -1
1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = -1

Add '-2m' to each side of the equation.
1X + 2m + 4mX + 2mx + -8m2 + -1x + -2m + -1xX = -1 + -2m

Reorder the terms:
1X + 2m + -2m + 4mX + 2mx + -8m2 + -1x + -1xX = -1 + -2m

Combine like terms: 2m + -2m = 0
1X + 0 + 4mX + 2mx + -8m2 + -1x + -1xX = -1 + -2m
1X + 4mX + 2mx + -8m2 + -1x + -1xX = -1 + -2m

Add '-2mx' to each side of the equation.
1X + 4mX + 2mx + -8m2 + -1x + -2mx + -1xX = -1 + -2m + -2mx

Reorder the terms:
1X + 4mX + 2mx + -2mx + -8m2 + -1x + -1xX = -1 + -2m + -2mx

Combine like terms: 2mx + -2mx = 0
1X + 4mX + 0 + -8m2 + -1x + -1xX = -1 + -2m + -2mx
1X + 4mX + -8m2 + -1x + -1xX = -1 + -2m + -2mx

Add '8m2' to each side of the equation.
1X + 4mX + -8m2 + -1x + 8m2 + -1xX = -1 + -2m + -2mx + 8m2

Reorder the terms:
1X + 4mX + -8m2 + 8m2 + -1x + -1xX = -1 + -2m + -2mx + 8m2

Combine like terms: -8m2 + 8m2 = 0
1X + 4mX + 0 + -1x + -1xX = -1 + -2m + -2mx + 8m2
1X + 4mX + -1x + -1xX = -1 + -2m + -2mx + 8m2

Add 'x' to each side of the equation.
1X + 4mX + -1x + x + -1xX = -1 + -2m + -2mx + 8m2 + x

Combine like terms: -1x + x = 0
1X + 4mX + 0 + -1xX = -1 + -2m + -2mx + 8m2 + x
1X + 4mX + -1xX = -1 + -2m + -2mx + 8m2 + x

Reorder the terms:
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = -1 + -2m + -2mx + 8m2 + x + 1 + 2m + 2mx + -8m2 + -1x

Reorder the terms:
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = -1 + 1 + -2m + 2m + -2mx + 2mx + 8m2 + -8m2 + x + -1x

Combine like terms: -1 + 1 = 0
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + -2m + 2m + -2mx + 2mx + 8m2 + -8m2 + x + -1x
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = -2m + 2m + -2mx + 2mx + 8m2 + -8m2 + x + -1x

Combine like terms: -2m + 2m = 0
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + -2mx + 2mx + 8m2 + -8m2 + x + -1x
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = -2mx + 2mx + 8m2 + -8m2 + x + -1x

Combine like terms: -2mx + 2mx = 0
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + 8m2 + -8m2 + x + -1x
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 8m2 + -8m2 + x + -1x

Combine like terms: 8m2 + -8m2 = 0
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0 + x + -1x
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = x + -1x

Combine like terms: x + -1x = 0
1 + 1X + 2m + 4mX + 2mx + -8m2 + -1x + -1xX = 0

The solution to this equation could not be determined.

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