x^2-2(3m-1)x+2m+3=0

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Solution for x^2-2(3m-1)x+2m+3=0 equation: 


Simplifying
x2 + -2(3m + -1) * x + 2m + 3 = 0

Reorder the terms:
x2 + -2(-1 + 3m) * x + 2m + 3 = 0

Reorder the terms for easier multiplication:
x2 + -2x(-1 + 3m) + 2m + 3 = 0
x2 + (-1 * -2x + 3m * -2x) + 2m + 3 = 0

Reorder the terms:
x2 + (-6mx + 2x) + 2m + 3 = 0
x2 + (-6mx + 2x) + 2m + 3 = 0

Reorder the terms:
3 + 2m + -6mx + 2x + x2 = 0

Solving
3 + 2m + -6mx + 2x + x2 = 0

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + 2m + -6mx + 2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 2m + -6mx + 2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2m + -6mx + 2x + x2 = 0 + -3
2m + -6mx + 2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2m + -6mx + 2x + x2 = -3

Add '-2x' to each side of the equation.
2m + -6mx + 2x + -2x + x2 = -3 + -2x

Combine like terms: 2x + -2x = 0
2m + -6mx + 0 + x2 = -3 + -2x
2m + -6mx + x2 = -3 + -2x

Add '-1x2' to each side of the equation.
2m + -6mx + x2 + -1x2 = -3 + -2x + -1x2

Combine like terms: x2 + -1x2 = 0
2m + -6mx + 0 = -3 + -2x + -1x2
2m + -6mx = -3 + -2x + -1x2

Reorder the terms:
3 + 2m + -6mx + 2x + x2 = -3 + -2x + -1x2 + 3 + 2x + x2

Reorder the terms:
3 + 2m + -6mx + 2x + x2 = -3 + 3 + -2x + 2x + -1x2 + x2

Combine like terms: -3 + 3 = 0
3 + 2m + -6mx + 2x + x2 = 0 + -2x + 2x + -1x2 + x2
3 + 2m + -6mx + 2x + x2 = -2x + 2x + -1x2 + x2

Combine like terms: -2x + 2x = 0
3 + 2m + -6mx + 2x + x2 = 0 + -1x2 + x2
3 + 2m + -6mx + 2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3 + 2m + -6mx + 2x + x2 = 0

The solution to this equation could not be determined.

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