(Ax+b)(bx+a)=10x+10x+cx+10

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Solution for (Ax+b)(bx+a)=10x+10x+cx+10 equation: 


Simplifying
(Ax + b)(bx + a) = 10x + 10x + cx + 10

Reorder the terms:
(b + xA)(bx + a) = 10x + 10x + cx + 10

Reorder the terms:
(b + xA)(a + bx) = 10x + 10x + cx + 10

Multiply (b + xA) * (a + bx)
(b(a + bx) + xA(a + bx)) = 10x + 10x + cx + 10
((a * b + bx * b) + xA(a + bx)) = 10x + 10x + cx + 10
((ab + b2x) + xA(a + bx)) = 10x + 10x + cx + 10
(ab + b2x + (a * xA + bx * xA)) = 10x + 10x + cx + 10
(ab + b2x + (axA + bx2A)) = 10x + 10x + cx + 10

Reorder the terms:
(ab + axA + bx2A + b2x) = 10x + 10x + cx + 10
(ab + axA + bx2A + b2x) = 10x + 10x + cx + 10

Reorder the terms:
ab + axA + bx2A + b2x = 10 + cx + 10x + 10x

Combine like terms: 10x + 10x = 20x
ab + axA + bx2A + b2x = 10 + cx + 20x

Solving
ab + axA + bx2A + b2x = 10 + cx + 20x

Solving for variable 'a'.

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

Add '-1bx2A' to each side of the equation.
ab + axA + bx2A + -1bx2A + b2x = 10 + cx + -1bx2A + 20x

Combine like terms: bx2A + -1bx2A = 0
ab + axA + 0 + b2x = 10 + cx + -1bx2A + 20x
ab + axA + b2x = 10 + cx + -1bx2A + 20x

Reorder the terms:
ab + axA + b2x = 10 + -1bx2A + cx + 20x

Add '-1b2x' to each side of the equation.
ab + axA + b2x + -1b2x = 10 + -1bx2A + cx + -1b2x + 20x

Combine like terms: b2x + -1b2x = 0
ab + axA + 0 = 10 + -1bx2A + cx + -1b2x + 20x
ab + axA = 10 + -1bx2A + cx + -1b2x + 20x

Reorder the terms:
ab + axA = 10 + -1bx2A + -1b2x + cx + 20x

Reorder the terms:
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 10 + -1bx2A + -1b2x + cx + 20x + -10 + bx2A + b2x + -1cx + -20x

Reorder the terms:
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 10 + -10 + -1bx2A + bx2A + -1b2x + b2x + cx + -1cx + 20x + -20x

Combine like terms: 10 + -10 = 0
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 0 + -1bx2A + bx2A + -1b2x + b2x + cx + -1cx + 20x + -20x
-10 + ab + axA + bx2A + b2x + -1cx + -20x = -1bx2A + bx2A + -1b2x + b2x + cx + -1cx + 20x + -20x

Combine like terms: -1bx2A + bx2A = 0
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 0 + -1b2x + b2x + cx + -1cx + 20x + -20x
-10 + ab + axA + bx2A + b2x + -1cx + -20x = -1b2x + b2x + cx + -1cx + 20x + -20x

Combine like terms: -1b2x + b2x = 0
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 0 + cx + -1cx + 20x + -20x
-10 + ab + axA + bx2A + b2x + -1cx + -20x = cx + -1cx + 20x + -20x

Combine like terms: cx + -1cx = 0
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 0 + 20x + -20x
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 20x + -20x

Combine like terms: 20x + -20x = 0
-10 + ab + axA + bx2A + b2x + -1cx + -20x = 0

The solution to this equation could not be determined.

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