## The system of equations (64 equations -12 unknown) solution help

Regards,
when programming an application I faced with the following system of equations
Code:
n1=i1*i5*i9
n2=i1*i5*i10
n3=i1*i5*i11
n4=i1*i5*i12
n5=i1*i6*i9
n6=i1*i6*i10
n7=i1*i6*i11
n8=i1*i6*i12
n9=i1*i7*i9
n10=i1*i7*i10
n11=i1*i7*i11
n12=i1*i7*i12
n13=i1*i8*i9
n14=i1*i8*i10
n15=i1*i8*i11
n16=i1*i8*i12
n17=i2*i5*i9
n18=i2*i5*i10
n19=i2*i5*i11
n20=i2*i5*i12
n21=i2*i6*i9
n22=i2*i6*i10
n23=i2*i6*i11
n24=i2*i6*i12
n25=i2*i7*i9
n26=i2*i7*i10
n27=i2*i7*i11
n28=i2*i7*i12
n29=i2*i8*i9
n30=i2*i8*i10
n31=i2*i8*i11
n32=i2*i8*i12
n33=i3*i5*i9
n34=i3*i5*i10
n35=i3*i5*i11
n36=i3*i5*i12
n37=i3*i6*i9
n38=i3*i6*i10
n39=i3*i6*i11
n40=i3*i6*i12
n41=i3*i7*i9
n42=i3*i7*i10
n43=i3*i7*i11
n44=i3*i7*i12
n45=i3*i8*i9
n46=i3*i8*i10
n47=i3*i8*i11
n48=i3*i8*i12
n49=i4*i5*i9
n50=i4*i5*i10
n51=i4*i5*i11
n52=i4*i5*i12
n53=i4*i6*i9
n54=i4*i6*i10
n55=i4*i6*i11
n56=i4*i6*i12
n57=i4*i7*i9
n58=i4*i7*i10
n59=i4*i7*i11
n60=i4*i7*i12
n61=i4*i8*i9
n62=i4*i8*i10
n63=i4*i8*i11
n64=i4*i8*i12
The system of equations resulting from these matrix, with permutation of all elements

Code:
i1   i5    i9
i2   i6    i10
i3   i7    i11
i4   i8    i12

In the above equations, n (n1, n2 ..., n64) are familiar values, while the i (i1, i2, ..., i12) are unknown values

The whole day i am trying to solve this, but no success.
Is it possible to solve this system of equations?
if so. How?