(ax+c)(bx+d)=(bx+c)(ax+d)

Solution for (ax+c)(bx+d)=(bx+c)(ax+d) equation:

Simplifying
(ax + c)(bx + d) = (bx + c)(ax + d)

Multiply (ax + c) * (bx + d)
(ax(bx + d) + c(bx + d)) = (bx + c)(ax + d)
((bx * ax + d * ax) + c(bx + d)) = (bx + c)(ax + d)
((abx2 + adx) + c(bx + d)) = (bx + c)(ax + d)
(abx2 + adx + (bx * c + d * c)) = (bx + c)(ax + d)
(abx2 + adx + (bcx + cd)) = (bx + c)(ax + d)
(abx2 + adx + bcx + cd) = (bx + c)(ax + d)

Multiply (bx + c) * (ax + d)
abx2 + adx + bcx + cd = (bx(ax + d) + c(ax + d))
abx2 + adx + bcx + cd = ((ax * bx + d * bx) + c(ax + d))
abx2 + adx + bcx + cd = ((abx2 + bdx) + c(ax + d))
abx2 + adx + bcx + cd = (abx2 + bdx + (ax * c + d * c))
abx2 + adx + bcx + cd = (abx2 + bdx + (acx + cd))

Reorder the terms:
abx2 + adx + bcx + cd = (abx2 + acx + bdx + cd)
abx2 + adx + bcx + cd = (abx2 + acx + bdx + cd)

Add '-1abx2' to each side of the equation.
abx2 + adx + bcx + -1abx2 + cd = abx2 + acx + bdx + -1abx2 + cd

Reorder the terms:
abx2 + -1abx2 + adx + bcx + cd = abx2 + acx + bdx + -1abx2 + cd

Combine like terms: abx2 + -1abx2 = 0
0 + adx + bcx + cd = abx2 + acx + bdx + -1abx2 + cd
adx + bcx + cd = abx2 + acx + bdx + -1abx2 + cd

Reorder the terms:
adx + bcx + cd = abx2 + -1abx2 + acx + bdx + cd

Combine like terms: abx2 + -1abx2 = 0
adx + bcx + cd = 0 + acx + bdx + cd
adx + bcx + cd = acx + bdx + cd

Add '-1cd' to each side of the equation.
adx + bcx + cd + -1cd = acx + bdx + cd + -1cd

Combine like terms: cd + -1cd = 0
adx + bcx + 0 = acx + bdx + cd + -1cd
adx + bcx = acx + bdx + cd + -1cd

Combine like terms: cd + -1cd = 0
adx + bcx = acx + bdx + 0
adx + bcx = acx + bdx

Solving
adx + bcx = acx + bdx

Solving for variable 'a'.

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

Add '-1acx' to each side of the equation.
adx + -1acx + bcx = acx + -1acx + bdx

Reorder the terms:
-1acx + adx + bcx = acx + -1acx + bdx

Combine like terms: acx + -1acx = 0
-1acx + adx + bcx = 0 + bdx
-1acx + adx + bcx = bdx

Add '-1bcx' to each side of the equation.
-1acx + adx + bcx + -1bcx = -1bcx + bdx

Combine like terms: bcx + -1bcx = 0
-1acx + adx + 0 = -1bcx + bdx
-1acx + adx = -1bcx + bdx

Reorder the terms:
-1acx + adx + bcx + -1bdx = -1bcx + bcx + bdx + -1bdx

Combine like terms: -1bcx + bcx = 0
-1acx + adx + bcx + -1bdx = 0 + bdx + -1bdx
-1acx + adx + bcx + -1bdx = bdx + -1bdx

Combine like terms: bdx + -1bdx = 0
-1acx + adx + bcx + -1bdx = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ac + ad + bc + -1bd) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1ac + ad + bc + -1bd)' equal to zero and attempt to solve:

Simplifying
-1ac + ad + bc + -1bd = 0

Solving
-1ac + ad + bc + -1bd = 0

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

Add '-1bc' to each side of the equation.
-1ac + ad + bc + -1bc + -1bd = 0 + -1bc

Combine like terms: bc + -1bc = 0
-1ac + ad + 0 + -1bd = 0 + -1bc
-1ac + ad + -1bd = 0 + -1bc
Remove the zero:
-1ac + ad + -1bd = -1bc

Add 'bd' to each side of the equation.
-1ac + ad + -1bd + bd = -1bc + bd

Combine like terms: -1bd + bd = 0
-1ac + ad + 0 = -1bc + bd
-1ac + ad = -1bc + bd

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.