I'm doing this problem correctly but I can't get the right answer

A spaceship of mass 2.00×106 is cruising at a speed of 5.70×106 when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.20×105 , is blown straight backward with a speed of 2.30×106 . A second piece, with mass 7.70×105 , continues forward at 1.10×106

I am using MV=m_1*v_1 + m_2*v_2 + m_3*v_3

i am solving for m_3 by doing M=m_1 + m_2 + m_3 and solving for m+3

for some reason I am doing something wrong with the algebra or arithmetic. I have tried this problem over 5 times, and I really need the correct answer within the next 2 tries. can someone please correct my approach or do the right algebra or arithmetic?

I assume you need to calculate V3?

M = m1 + m2 + m3

20×10^5 = 5.20×10^5 + 7.7×10^5 + m3

m3 = 7.1×10^5

Then u can find v3

MV = m1v1 + m2v2 + m3v3

2.00×106 × 5.70×106 = - (5.20×105 × 2.30×106) + 7.70×105 × 1.10×106 + 7.1×10^5 × v3

11.4 × 1012 = -11.96 × 1011 + 8.47 × 1011 + 7.1 × 105 × v3

11.4 × 1012 + 3.49 × 1011 = 7.1 × 105 × v3

117.49 × 1011 / 7.1 × 105 = v3

v3 = 16.54 × 106