just solve the equation step by step
0.1(t+0.5) +0.2t =0.3(t-0.4)
0.1 (t + 0.5) + 0.2t = 0.3 (t - 0.4);
0.1t + 0.05 + 0.2t = 0.3t - 0.12;
0.3t + 0.05 = 0.3t - 0.12;
0.05 = 0.12 which is obviously not true.
Hence there is no solution to this problem.
1) Distribute 0.1 into (t+0.5) on the left side and 0.3 into (t-0.4) on the right side.
2) Move all terms with t factor to the left, move all other terms to the right.
3) Collect like terms.
4) After step 3 you shall obtain equation of the form a*t=b. Its solution is t=b/a if a≠0. If a=0 and b≠0, then there is no solution. If a=0 and b=0 then there are infinitely many solutions, that is any t is the solution.