(x-a)(x-b)=x^2+x+c

Solution for (x-a)(x-b)=x^2+x+c equation:

Simplifying
(x + -1a)(x + -1b) = x2 + x + c

Reorder the terms:
(-1a + x)(x + -1b) = x2 + x + c

Reorder the terms:
(-1a + x)(-1b + x) = x2 + x + c

Multiply (-1a + x) * (-1b + x)
(-1a * (-1b + x) + x(-1b + x)) = x2 + x + c
((-1b * -1a + x * -1a) + x(-1b + x)) = x2 + x + c
((1ab + -1ax) + x(-1b + x)) = x2 + x + c
(1ab + -1ax + (-1b * x + x * x)) = x2 + x + c
(1ab + -1ax + (-1bx + x2)) = x2 + x + c
(1ab + -1ax + -1bx + x2) = x2 + x + c

Reorder the terms:
1ab + -1ax + -1bx + x2 = c + x + x2

Add '-1x2' to each side of the equation.
1ab + -1ax + -1bx + x2 + -1x2 = c + x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1ab + -1ax + -1bx + 0 = c + x + x2 + -1x2
1ab + -1ax + -1bx = c + x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1ab + -1ax + -1bx = c + x + 0
1ab + -1ax + -1bx = c + x

Solving
1ab + -1ax + -1bx = c + x

Solving for variable 'a'.

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

Add 'bx' to each side of the equation.
1ab + -1ax + -1bx + bx = c + bx + x

Combine like terms: -1bx + bx = 0
1ab + -1ax + 0 = c + bx + x
1ab + -1ax = c + bx + x

Reorder the terms:
1ab + -1ax = bx + c + x

Reorder the terms:
1ab + -1ax + -1bx + -1c + -1x = bx + -1bx + c + -1c + x + -1x

Combine like terms: bx + -1bx = 0
1ab + -1ax + -1bx + -1c + -1x = 0 + c + -1c + x + -1x
1ab + -1ax + -1bx + -1c + -1x = c + -1c + x + -1x

Combine like terms: c + -1c = 0
1ab + -1ax + -1bx + -1c + -1x = 0 + x + -1x
1ab + -1ax + -1bx + -1c + -1x = x + -1x

Combine like terms: x + -1x = 0
1ab + -1ax + -1bx + -1c + -1x = 0

The solution to this equation could not be determined.