(m-2)x^2+(3m-5)x+3=0

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Solution for (m-2)x^2+(3m-5)x+3=0 equation: 


Simplifying
(m + -2) * x2 + (3m + -5) * x + 3 = 0

Reorder the terms:
(-2 + m) * x2 + (3m + -5) * x + 3 = 0

Reorder the terms for easier multiplication:
x2(-2 + m) + (3m + -5) * x + 3 = 0
(-2 * x2 + m * x2) + (3m + -5) * x + 3 = 0

Reorder the terms:
(mx2 + -2x2) + (3m + -5) * x + 3 = 0
(mx2 + -2x2) + (3m + -5) * x + 3 = 0

Reorder the terms:
mx2 + -2x2 + (-5 + 3m) * x + 3 = 0

Reorder the terms for easier multiplication:
mx2 + -2x2 + x(-5 + 3m) + 3 = 0
mx2 + -2x2 + (-5 * x + 3m * x) + 3 = 0

Reorder the terms:
mx2 + -2x2 + (3mx + -5x) + 3 = 0
mx2 + -2x2 + (3mx + -5x) + 3 = 0

Reorder the terms:
3 + 3mx + mx2 + -5x + -2x2 = 0

Solving
3 + 3mx + mx2 + -5x + -2x2 = 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 + 3mx + mx2 + -5x + -3 + -2x2 = 0 + -3

Reorder the terms:
3 + -3 + 3mx + mx2 + -5x + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3mx + mx2 + -5x + -2x2 = 0 + -3
3mx + mx2 + -5x + -2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
3mx + mx2 + -5x + -2x2 = -3

Add '5x' to each side of the equation.
3mx + mx2 + -5x + 5x + -2x2 = -3 + 5x

Combine like terms: -5x + 5x = 0
3mx + mx2 + 0 + -2x2 = -3 + 5x
3mx + mx2 + -2x2 = -3 + 5x

Add '2x2' to each side of the equation.
3mx + mx2 + -2x2 + 2x2 = -3 + 5x + 2x2

Combine like terms: -2x2 + 2x2 = 0
3mx + mx2 + 0 = -3 + 5x + 2x2
3mx + mx2 = -3 + 5x + 2x2

Reorder the terms:
3 + 3mx + mx2 + -5x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Reorder the terms:
3 + 3mx + mx2 + -5x + -2x2 = -3 + 3 + 5x + -5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
3 + 3mx + mx2 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
3 + 3mx + mx2 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
3 + 3mx + mx2 + -5x + -2x2 = 0 + 2x2 + -2x2
3 + 3mx + mx2 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 3mx + mx2 + -5x + -2x2 = 0

The solution to this equation could not be determined.

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