3a+2z+1=3b+c

Solution for 3a+2z+1=3b+c equation:

Simplifying
3a + 2z + 1 = 3b + c

Reorder the terms:
1 + 3a + 2z = 3b + c

Solving
1 + 3a + 2z = 3b + c

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + 3a + -1 + 2z = 3b + -1 + c

Reorder the terms:
1 + -1 + 3a + 2z = 3b + -1 + c

Combine like terms: 1 + -1 = 0
0 + 3a + 2z = 3b + -1 + c
3a + 2z = 3b + -1 + c

Reorder the terms:
3a + 2z = -1 + 3b + c

Add '-2z' to each side of the equation.
3a + 2z + -2z = -1 + 3b + c + -2z

Combine like terms: 2z + -2z = 0
3a + 0 = -1 + 3b + c + -2z
3a = -1 + 3b + c + -2z

Divide each side by '3'.
a = -0.3333333333 + b + 0.3333333333c + -0.6666666667z

Simplifying
a = -0.3333333333 + b + 0.3333333333c + -0.6666666667z