ax^2-(3a-1)(x-2)+2a=0

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


Simplifying
ax2 + -1(3a + -1)(x + -2) + 2a = 0

Reorder the terms:
ax2 + -1(-1 + 3a)(x + -2) + 2a = 0

Reorder the terms:
ax2 + -1(-1 + 3a)(-2 + x) + 2a = 0

Multiply (-1 + 3a) * (-2 + x)
ax2 + -1(-1(-2 + x) + 3a * (-2 + x)) + 2a = 0
ax2 + -1((-2 * -1 + x * -1) + 3a * (-2 + x)) + 2a = 0
ax2 + -1((2 + -1x) + 3a * (-2 + x)) + 2a = 0
ax2 + -1(2 + -1x + (-2 * 3a + x * 3a)) + 2a = 0
ax2 + -1(2 + -1x + (-6a + 3ax)) + 2a = 0

Reorder the terms:
ax2 + -1(2 + -6a + 3ax + -1x) + 2a = 0
ax2 + -1(2 + -6a + 3ax + -1x) + 2a = 0
ax2 + (2 * -1 + -6a * -1 + 3ax * -1 + -1x * -1) + 2a = 0
ax2 + (-2 + 6a + -3ax + 1x) + 2a = 0

Reorder the terms:
-2 + 6a + 2a + -3ax + ax2 + 1x = 0

Combine like terms: 6a + 2a = 8a
-2 + 8a + -3ax + ax2 + 1x = 0

Solving
-2 + 8a + -3ax + ax2 + 1x = 0

Solving for variable 'a'.

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

Add '2' to each side of the equation.
-2 + 8a + -3ax + ax2 + 2 + 1x = 0 + 2

Reorder the terms:
-2 + 2 + 8a + -3ax + ax2 + 1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8a + -3ax + ax2 + 1x = 0 + 2
8a + -3ax + ax2 + 1x = 0 + 2

Combine like terms: 0 + 2 = 2
8a + -3ax + ax2 + 1x = 2

Add '-1x' to each side of the equation.
8a + -3ax + ax2 + 1x + -1x = 2 + -1x

Combine like terms: 1x + -1x = 0
8a + -3ax + ax2 + 0 = 2 + -1x
8a + -3ax + ax2 = 2 + -1x

Reorder the terms:
-2 + 8a + -3ax + ax2 + x = 2 + -1x + -2 + x

Reorder the terms:
-2 + 8a + -3ax + ax2 + x = 2 + -2 + -1x + x

Combine like terms: 2 + -2 = 0
-2 + 8a + -3ax + ax2 + x = 0 + -1x + x
-2 + 8a + -3ax + ax2 + x = -1x + x

Combine like terms: -1x + x = 0
-2 + 8a + -3ax + ax2 + x = 0

The solution to this equation could not be determined.

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