(2x+1)(ax+b)=6x^2+5x+c

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Solution for (2x+1)(ax+b)=6x^2+5x+c equation: 


Simplifying
(2x + 1)(ax + b) = 6x2 + 5x + c

Reorder the terms:
(1 + 2x)(ax + b) = 6x2 + 5x + c

Multiply (1 + 2x) * (ax + b)
(1(ax + b) + 2x * (ax + b)) = 6x2 + 5x + c
((ax * 1 + b * 1) + 2x * (ax + b)) = 6x2 + 5x + c
((1ax + 1b) + 2x * (ax + b)) = 6x2 + 5x + c
(1ax + 1b + (ax * 2x + b * 2x)) = 6x2 + 5x + c
(1ax + 1b + (2ax2 + 2bx)) = 6x2 + 5x + c

Reorder the terms:
(1ax + 2ax2 + 1b + 2bx) = 6x2 + 5x + c
(1ax + 2ax2 + 1b + 2bx) = 6x2 + 5x + c

Reorder the terms:
1ax + 2ax2 + 1b + 2bx = c + 5x + 6x2

Solving
1ax + 2ax2 + 1b + 2bx = c + 5x + 6x2

Solving for variable 'a'.

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

Add '-1b' to each side of the equation.
1ax + 2ax2 + 1b + -1b + 2bx = c + 5x + -1b + 6x2

Combine like terms: 1b + -1b = 0
1ax + 2ax2 + 0 + 2bx = c + 5x + -1b + 6x2
1ax + 2ax2 + 2bx = c + 5x + -1b + 6x2

Reorder the terms:
1ax + 2ax2 + 2bx = -1b + c + 5x + 6x2

Add '-2bx' to each side of the equation.
1ax + 2ax2 + 2bx + -2bx = -1b + c + 5x + -2bx + 6x2

Combine like terms: 2bx + -2bx = 0
1ax + 2ax2 + 0 = -1b + c + 5x + -2bx + 6x2
1ax + 2ax2 = -1b + c + 5x + -2bx + 6x2

Reorder the terms:
1ax + 2ax2 = -1b + -2bx + c + 5x + 6x2

Reorder the terms:
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = -1b + b + -2bx + 2bx + c + -1c + 5x + -5x + 6x2 + -6x2

Combine like terms: -1b + b = 0
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 0 + -2bx + 2bx + c + -1c + 5x + -5x + 6x2 + -6x2
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = -2bx + 2bx + c + -1c + 5x + -5x + 6x2 + -6x2

Combine like terms: -2bx + 2bx = 0
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 0 + c + -1c + 5x + -5x + 6x2 + -6x2
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = c + -1c + 5x + -5x + 6x2 + -6x2

Combine like terms: c + -1c = 0
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 5x + -5x + 6x2 + -6x2

Combine like terms: 5x + -5x = 0
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 0 + 6x2 + -6x2
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1ax + 2ax2 + b + 2bx + -1c + -5x + -6x2 = 0

The solution to this equation could not be determined.

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