Investment firm Energy Capital Partners has increased its offer for EnergySolutions Inc. by 40 cents or $4.15 per share.

The new offer, which came almost three months after its initial bid, now has the backing of its largest shareholder Carlson P. Capital LP, EnergySolutions said.

Energy Capital's new offer now values EnergySolution's equity at about $378 million.

Nuclear waste manager EnergySolutions had agreed to be taken private to increase its ability to invest in its nuclear plant decommissioning business.

However, aside from EnergySolution's shareholders, the deal needs to have the approval of the   Nuclear Regulatory Commission and the State of Utah.