Question

a\cdot(t+z) = 45z+67

Answer 1

You can rearrange the equation a(t + z) = 45z + 67 to solve for any one variable in terms of the others. Important special cases (division by zero) are noted.

1) Solve for a:
- If t + z ≠ 0, a = (45z + 67)/(t + z).
- If t + z = 0 then LHS = 0, so the equation requires 45z + 67 = 0 (i.e. z = −67/45). If that holds any a works; otherwise there is no solution.

2) Solve for t:
- If a ≠ 0, t = (45z + 67)/a − z.
- If a = 0 then 0 = 45z + 67, so z must be −67/45 for consistency; if z = −67/45 any t is allowed, otherwise no solution.

3) Solve for z:
Rewrite as az − 45z = 67 − at, so z(a − 45) = 67 − at.
- If a ≠ 45, z = (67 − at)/(a − 45).
- If a = 45 then the equation reduces to 45t = 67, so t must equal 67/45; if t = 67/45 any z is allowed, otherwise no solution.

Tell me which variable you want isolated or whether you want integer/real solutions.