1. Stating the problem: Solve for the variables in the equation $$2x(5t+2f)=10$$. 2. Expand the left-hand side: Multiply 2x with each term inside the parentheses. $$2x \times 5t + 2x \times 2f = 10$$ $$10xt + 4xf = 10$$ 3. Factor the left-hand side if needed or isolate terms (depends on what variables to solve for). Without specific instructions to solve for one variable or values of others, we can express the equation as: $$10xt + 4xf = 10$$ 4. Explanation: This relates the product of $x$ with $t$ and $f$. - To solve for $x$: $$x(10t + 4f) = 10$$ $$x = \frac{10}{10t + 4f}$$ 5. Final answer: $$x = \frac{10}{10t + 4f}$$ or equivalently $$2x(5t + 2f) = 10$$ can be solved for $x$ as above given $t$ and $f$ are not zero.