#### Answer

$c=2$

#### Work Step by Step

We start with the given equation: $4c-7=-c+3$
We subtract $4c$ from both sides of the equation: $4c-4c-7=-4c-c+3$
We subtract $3$ from both sides of the equation: $4c-4c-7-3=-4c-c+3-3$
We combine like terms on both sides of the equation: $-10=-5c$
We divide by $-5$ on both sides of the equation: $c=\frac{-10}{-5}=2$