The expression we have is:
[tex]\frac{3}{5}t+7=-8[/tex]Step 1. Substract 7 from both sides of the equation:
[tex]\begin{gathered} \frac{3}{5}t+7-7=-8-7 \\ \frac{3}{5}t=-15 \end{gathered}[/tex]Step 2. Multiply both sides by 5/3 to eliminat the 3/5 on the left:
[tex]\frac{5}{3}\times\frac{3}{5}t=\frac{5}{3}\times(-15)[/tex]On the left we are left only with t:
[tex]t=\frac{5}{3}\times(-15)[/tex]Step 3. Solve the multiplication on the right side:
[tex]\begin{gathered} t=-\frac{5\times15}{3} \\ t=-\frac{75}{3} \end{gathered}[/tex]Step 4. Solve the division to find the final value of t:
[tex]t=-25[/tex]