Solve t+(b+c)=(a+b)+c

$$t + ( b + c ) = ( a + b ) + c$$

Solve for a

$$a=t$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$a+b+c=t+b+c$$

Subtract b from both sides.

$$a+c=t+b+c-b$$

Combine b and -b to get 0.

$$a+c=t+c$$

Subtract c from both sides.

$$a=t+c-c$$

Combine c and -c to get 0.

$$a=t$$

Solve for b (complex solution)

$$b\in \mathrm{C}$$

$$t=a$$

Solve for b

$$b\in \mathrm{R}$$

$$t=a$$