6x^2-x-a=(ax+1)(3x-2)

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Solution for 6x^2-x-a=(ax+1)(3x-2) equation: 


Simplifying
6x2 + -1x + -1a = (ax + 1)(3x + -2)

Reorder the terms:
-1a + -1x + 6x2 = (ax + 1)(3x + -2)

Reorder the terms:
-1a + -1x + 6x2 = (1 + ax)(3x + -2)

Reorder the terms:
-1a + -1x + 6x2 = (1 + ax)(-2 + 3x)

Multiply (1 + ax) * (-2 + 3x)
-1a + -1x + 6x2 = (1(-2 + 3x) + ax(-2 + 3x))
-1a + -1x + 6x2 = ((-2 * 1 + 3x * 1) + ax(-2 + 3x))
-1a + -1x + 6x2 = ((-2 + 3x) + ax(-2 + 3x))
-1a + -1x + 6x2 = (-2 + 3x + (-2 * ax + 3x * ax))
-1a + -1x + 6x2 = (-2 + 3x + (-2ax + 3ax2))

Reorder the terms:
-1a + -1x + 6x2 = (-2 + -2ax + 3ax2 + 3x)
-1a + -1x + 6x2 = (-2 + -2ax + 3ax2 + 3x)

Solving
-1a + -1x + 6x2 = -2 + -2ax + 3ax2 + 3x

Solving for variable 'a'.

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

Add '2ax' to each side of the equation.
-1a + -1x + 2ax + 6x2 = -2 + -2ax + 3ax2 + 2ax + 3x

Reorder the terms:
-1a + 2ax + -1x + 6x2 = -2 + -2ax + 3ax2 + 2ax + 3x

Reorder the terms:
-1a + 2ax + -1x + 6x2 = -2 + -2ax + 2ax + 3ax2 + 3x

Combine like terms: -2ax + 2ax = 0
-1a + 2ax + -1x + 6x2 = -2 + 0 + 3ax2 + 3x
-1a + 2ax + -1x + 6x2 = -2 + 3ax2 + 3x

Add '-3ax2' to each side of the equation.
-1a + 2ax + -1x + -3ax2 + 6x2 = -2 + 3ax2 + -3ax2 + 3x

Reorder the terms:
-1a + 2ax + -3ax2 + -1x + 6x2 = -2 + 3ax2 + -3ax2 + 3x

Combine like terms: 3ax2 + -3ax2 = 0
-1a + 2ax + -3ax2 + -1x + 6x2 = -2 + 0 + 3x
-1a + 2ax + -3ax2 + -1x + 6x2 = -2 + 3x

Add 'x' to each side of the equation.
-1a + 2ax + -3ax2 + -1x + x + 6x2 = -2 + 3x + x

Combine like terms: -1x + x = 0
-1a + 2ax + -3ax2 + 0 + 6x2 = -2 + 3x + x
-1a + 2ax + -3ax2 + 6x2 = -2 + 3x + x

Combine like terms: 3x + x = 4x
-1a + 2ax + -3ax2 + 6x2 = -2 + 4x

Add '-6x2' to each side of the equation.
-1a + 2ax + -3ax2 + 6x2 + -6x2 = -2 + 4x + -6x2

Combine like terms: 6x2 + -6x2 = 0
-1a + 2ax + -3ax2 + 0 = -2 + 4x + -6x2
-1a + 2ax + -3ax2 = -2 + 4x + -6x2

Reorder the terms:
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = -2 + 4x + -6x2 + 2 + -4x + 6x2

Reorder the terms:
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = -2 + 2 + 4x + -4x + -6x2 + 6x2

Combine like terms: -2 + 2 = 0
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = 0 + 4x + -4x + -6x2 + 6x2
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = 4x + -4x + -6x2 + 6x2

Combine like terms: 4x + -4x = 0
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = 0 + -6x2 + 6x2
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
2 + -1a + 2ax + -3ax2 + -4x + 6x2 = 0

The solution to this equation could not be determined.

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