(x+a)(x+b)-ab=(x+c)(x-c)+c(a+c)

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

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

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

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

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

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

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

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

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

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

Reorder the terms:
ax + bx + x2 = ((cx + -1c2) + x(-1c + x)) + c(a + c)
ax + bx + x2 = ((cx + -1c2) + x(-1c + x)) + c(a + c)
ax + bx + x2 = (cx + -1c2 + (-1c * x + x * x)) + c(a + c)
ax + bx + x2 = (cx + -1c2 + (-1cx + x2)) + c(a + c)

Reorder the terms:
ax + bx + x2 = (cx + -1cx + -1c2 + x2) + c(a + c)

Combine like terms: cx + -1cx = 0
ax + bx + x2 = (0 + -1c2 + x2) + c(a + c)
ax + bx + x2 = (-1c2 + x2) + c(a + c)
ax + bx + x2 = -1c2 + x2 + (a * c + c * c)
ax + bx + x2 = -1c2 + x2 + (ac + c2)

Reorder the terms:
ax + bx + x2 = ac + -1c2 + c2 + x2

Combine like terms: -1c2 + c2 = 0
ax + bx + x2 = ac + 0 + x2
ax + bx + x2 = ac + x2

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

Combine like terms: x2 + -1x2 = 0
ax + bx + 0 = ac + x2 + -1x2
ax + bx = ac + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ax + bx = ac + 0
ax + bx = ac

Solving
ax + bx = ac

Solving for variable 'a'.

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

Add '-1ac' to each side of the equation.
ax + -1ac + bx = ac + -1ac

Reorder the terms:
-1ac + ax + bx = ac + -1ac

Combine like terms: ac + -1ac = 0
-1ac + ax + bx = 0

Add '-1bx' to each side of the equation.
-1ac + ax + bx + -1bx = 0 + -1bx

Combine like terms: bx + -1bx = 0
-1ac + ax + 0 = 0 + -1bx
-1ac + ax = 0 + -1bx
Remove the zero:
-1ac + ax = -1bx

Combine like terms: -1bx + bx = 0
-1ac + ax + bx = 0

The solution to this equation could not be determined.