(x+a)(x+b)=(x+c)(x+d)

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

Simplifying
(x + a)(x + b) = (x + c)(x + d)

Reorder the terms:
(a + x)(x + b) = (x + c)(x + d)

Reorder the terms:
(a + x)(b + x) = (x + c)(x + d)

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

Reorder the terms:
ab + ax + bx + x2 = (c + x)(x + d)

Reorder the terms:
ab + ax + bx + x2 = (c + x)(d + x)

Multiply (c + x) * (d + x)
ab + ax + bx + x2 = (c(d + x) + x(d + x))
ab + ax + bx + x2 = ((d * c + x * c) + x(d + x))
ab + ax + bx + x2 = ((cd + cx) + x(d + x))
ab + ax + bx + x2 = (cd + cx + (d * x + x * x))
ab + ax + bx + x2 = (cd + cx + (dx + x2))
ab + ax + bx + x2 = (cd + cx + dx + x2)

Add '-1x2' to each side of the equation.
ab + ax + bx + x2 + -1x2 = cd + cx + dx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx + 0 = cd + cx + dx + x2 + -1x2
ab + ax + bx = cd + cx + dx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
ab + ax + bx = cd + cx + dx + 0
ab + ax + bx = cd + cx + dx

Solving
ab + ax + bx = cd + cx + dx

Solving for variable 'a'.

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

Add '-1bx' to each side of the equation.
ab + ax + bx + -1bx = cd + cx + -1bx + dx

Combine like terms: bx + -1bx = 0
ab + ax + 0 = cd + cx + -1bx + dx
ab + ax = cd + cx + -1bx + dx

Reorder the terms:
ab + ax = -1bx + cd + cx + dx

Reorder the terms:
ab + ax + bx + -1cd + -1cx + -1dx = -1bx + bx + cd + -1cd + cx + -1cx + dx + -1dx

Combine like terms: -1bx + bx = 0
ab + ax + bx + -1cd + -1cx + -1dx = 0 + cd + -1cd + cx + -1cx + dx + -1dx
ab + ax + bx + -1cd + -1cx + -1dx = cd + -1cd + cx + -1cx + dx + -1dx

Combine like terms: cd + -1cd = 0
ab + ax + bx + -1cd + -1cx + -1dx = 0 + cx + -1cx + dx + -1dx
ab + ax + bx + -1cd + -1cx + -1dx = cx + -1cx + dx + -1dx

Combine like terms: cx + -1cx = 0
ab + ax + bx + -1cd + -1cx + -1dx = 0 + dx + -1dx
ab + ax + bx + -1cd + -1cx + -1dx = dx + -1dx

Combine like terms: dx + -1dx = 0
ab + ax + bx + -1cd + -1cx + -1dx = 0

The solution to this equation could not be determined.