(x-2)*(2ax-3)+(x-2)*(-ax+1)=0

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


Simplifying
(x + -2)(2ax + -3) + (x + -2)(-1ax + 1) = 0

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

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

Multiply (-2 + x) * (-3 + 2ax)
(-2(-3 + 2ax) + x(-3 + 2ax)) + (x + -2)(-1ax + 1) = 0
((-3 * -2 + 2ax * -2) + x(-3 + 2ax)) + (x + -2)(-1ax + 1) = 0
((6 + -4ax) + x(-3 + 2ax)) + (x + -2)(-1ax + 1) = 0
(6 + -4ax + (-3 * x + 2ax * x)) + (x + -2)(-1ax + 1) = 0

Reorder the terms:
(6 + -4ax + (2ax2 + -3x)) + (x + -2)(-1ax + 1) = 0
(6 + -4ax + (2ax2 + -3x)) + (x + -2)(-1ax + 1) = 0
(6 + -4ax + 2ax2 + -3x) + (x + -2)(-1ax + 1) = 0

Reorder the terms:
6 + -4ax + 2ax2 + -3x + (-2 + x)(-1ax + 1) = 0

Reorder the terms:
6 + -4ax + 2ax2 + -3x + (-2 + x)(1 + -1ax) = 0

Multiply (-2 + x) * (1 + -1ax)
6 + -4ax + 2ax2 + -3x + (-2(1 + -1ax) + x(1 + -1ax)) = 0
6 + -4ax + 2ax2 + -3x + ((1 * -2 + -1ax * -2) + x(1 + -1ax)) = 0
6 + -4ax + 2ax2 + -3x + ((-2 + 2ax) + x(1 + -1ax)) = 0
6 + -4ax + 2ax2 + -3x + (-2 + 2ax + (1 * x + -1ax * x)) = 0

Reorder the terms:
6 + -4ax + 2ax2 + -3x + (-2 + 2ax + (-1ax2 + 1x)) = 0
6 + -4ax + 2ax2 + -3x + (-2 + 2ax + (-1ax2 + 1x)) = 0
6 + -4ax + 2ax2 + -3x + (-2 + 2ax + -1ax2 + 1x) = 0

Reorder the terms:
6 + -2 + -4ax + 2ax + 2ax2 + -1ax2 + -3x + 1x = 0

Combine like terms: 6 + -2 = 4
4 + -4ax + 2ax + 2ax2 + -1ax2 + -3x + 1x = 0

Combine like terms: -4ax + 2ax = -2ax
4 + -2ax + 2ax2 + -1ax2 + -3x + 1x = 0

Combine like terms: 2ax2 + -1ax2 = 1ax2
4 + -2ax + 1ax2 + -3x + 1x = 0

Combine like terms: -3x + 1x = -2x
4 + -2ax + 1ax2 + -2x = 0

Solving
4 + -2ax + 1ax2 + -2x = 0

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -2ax + 1ax2 + -4 + -2x = 0 + -4

Reorder the terms:
4 + -4 + -2ax + 1ax2 + -2x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2ax + 1ax2 + -2x = 0 + -4
-2ax + 1ax2 + -2x = 0 + -4

Combine like terms: 0 + -4 = -4
-2ax + 1ax2 + -2x = -4

Add '2x' to each side of the equation.
-2ax + 1ax2 + -2x + 2x = -4 + 2x

Combine like terms: -2x + 2x = 0
-2ax + 1ax2 + 0 = -4 + 2x
-2ax + 1ax2 = -4 + 2x

Reorder the terms:
4 + -2ax + 1ax2 + -2x = -4 + 2x + 4 + -2x

Reorder the terms:
4 + -2ax + 1ax2 + -2x = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
4 + -2ax + 1ax2 + -2x = 0 + 2x + -2x
4 + -2ax + 1ax2 + -2x = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + -2ax + 1ax2 + -2x = 0

The solution to this equation could not be determined.

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