To solve the equation $8 = 2(10 + 3c)$, let's follow these steps:

Step 1: Expand the equation

Distribute the $2$ on the right-hand side:

$8 = 2 \times 10 + 2 \times 3c$ $8 = 20 + 6c$

Step 2: Isolate the variable term

Subtract $20$ from both sides to isolate the term with $c$:

$8 - 20 = 6c$ $-12 = 6c$

Step 3: Solve for $c$

Divide both sides by $6$ to solve for $c$:

$c = \frac{-12}{6}$ $c = -2$

Final Answer:

$c = -2$.

Would you like a detailed explanation of any step, or have any questions?

Here are 5 related questions:

1. How do you solve for variables in equations with parentheses?
2. How can you verify your solution after solving for a variable?
3. What happens when equations include fractions or decimals?
4. How does factoring affect the process of solving equations?
5. How do you handle equations with multiple variables?

Tip: Always double-check your result by plugging the value of the variable back into the original equation to verify if both sides are equal.