Here's how I like to solve my equations: just walk around randomly until I trip over a solution!
⎕←⎕ucs 2∘⊥∘⌽¨ ↓7 (⊢⍴⍨⊣,⍨÷⍨∘≢) ⍎¨ '0001011001011100101110000111110', '0111010111011110101111010101101', '1100001100101110001011110011100', '0011100001110111010110001111110111011011'
