(3x-1)(ax+b)=12x^2-19x+c

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Solution for (3x-1)(ax+b)=12x^2-19x+c equation: 


Simplifying
(3x + -1)(ax + b) = 12x2 + -19x + c

Reorder the terms:
(-1 + 3x)(ax + b) = 12x2 + -19x + c

Multiply (-1 + 3x) * (ax + b)
(-1(ax + b) + 3x * (ax + b)) = 12x2 + -19x + c
((ax * -1 + b * -1) + 3x * (ax + b)) = 12x2 + -19x + c
((-1ax + -1b) + 3x * (ax + b)) = 12x2 + -19x + c
(-1ax + -1b + (ax * 3x + b * 3x)) = 12x2 + -19x + c
(-1ax + -1b + (3ax2 + 3bx)) = 12x2 + -19x + c

Reorder the terms:
(-1ax + 3ax2 + -1b + 3bx) = 12x2 + -19x + c
(-1ax + 3ax2 + -1b + 3bx) = 12x2 + -19x + c

Reorder the terms:
-1ax + 3ax2 + -1b + 3bx = c + -19x + 12x2

Solving
-1ax + 3ax2 + -1b + 3bx = c + -19x + 12x2

Solving for variable 'a'.

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

Add 'b' to each side of the equation.
-1ax + 3ax2 + -1b + b + 3bx = c + -19x + b + 12x2

Combine like terms: -1b + b = 0
-1ax + 3ax2 + 0 + 3bx = c + -19x + b + 12x2
-1ax + 3ax2 + 3bx = c + -19x + b + 12x2

Reorder the terms:
-1ax + 3ax2 + 3bx = b + c + -19x + 12x2

Add '-3bx' to each side of the equation.
-1ax + 3ax2 + 3bx + -3bx = b + c + -19x + -3bx + 12x2

Combine like terms: 3bx + -3bx = 0
-1ax + 3ax2 + 0 = b + c + -19x + -3bx + 12x2
-1ax + 3ax2 = b + c + -19x + -3bx + 12x2

Reorder the terms:
-1ax + 3ax2 = b + -3bx + c + -19x + 12x2

Reorder the terms:
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = b + -1b + -3bx + 3bx + c + -1c + -19x + 19x + 12x2 + -12x2

Combine like terms: b + -1b = 0
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 0 + -3bx + 3bx + c + -1c + -19x + 19x + 12x2 + -12x2
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = -3bx + 3bx + c + -1c + -19x + 19x + 12x2 + -12x2

Combine like terms: -3bx + 3bx = 0
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 0 + c + -1c + -19x + 19x + 12x2 + -12x2
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = c + -1c + -19x + 19x + 12x2 + -12x2

Combine like terms: c + -1c = 0
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 0 + -19x + 19x + 12x2 + -12x2
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = -19x + 19x + 12x2 + -12x2

Combine like terms: -19x + 19x = 0
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 0 + 12x2 + -12x2
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-1ax + 3ax2 + -1b + 3bx + -1c + 19x + -12x2 = 0

The solution to this equation could not be determined.

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