Variable $x$ cannot be equal to $-\frac{7}{2}$ since division by zero is not defined. Multiply both sides of the equation by $9000\left(2x+7\right)$, the least common multiple of $1125\left(7+2x\right),8$.
$$8\times 343=\left(2250x+7875\right)\times 16$$
Multiply $8$ and $343$ to get $2744$.
$$2744=\left(2250x+7875\right)\times 16$$
Use the distributive property to multiply $2250x+7875$ by $16$.
$$2744=36000x+126000$$
Swap sides so that all variable terms are on the left hand side.
$$36000x+126000=2744$$
Subtract $126000$ from both sides.
$$36000x=2744-126000$$
Subtract $126000$ from $2744$ to get $-123256$.
$$36000x=-123256$$
Divide both sides by $36000$.
$$x=\frac{-123256}{36000}$$
Reduce the fraction $\frac{-123256}{36000}$ to lowest terms by extracting and canceling out $8$.
