1. **State the problem:** Solve the equation $((4x+3)\cdot 2)+(6x+3)=69$ for $x$. 2. **Write the equation clearly:** $$ (4x+3)\cdot 2 + (6x+3) = 69 $$ 3. **Apply the distributive property:** $$ 2 \times (4x+3) = 8x + 6 $$ So the equation becomes: $$ 8x + 6 + 6x + 3 = 69 $$ 4. **Combine like terms:** $$ (8x + 6x) + (6 + 3) = 69 $$ $$ 14x + 9 = 69 $$ 5. **Isolate the variable term:** Subtract 9 from both sides: $$ 14x = 69 - 9 $$ $$ 14x = 60 $$ 6. **Solve for $x$:** Divide both sides by 14: $$ x = \frac{60}{14} = \frac{30}{7} $$ 7. **Final answer:** $$ x = \frac{30}{7} $$ or approximately $4.2857$. This means the value of $x$ that satisfies the original equation is $\frac{30}{7}$.