Solve the equation: `|[x+a, b,c],[a,x+b,c],[a,b,x+c]|=0 `

Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

If a+b+c=0, solve the equation: |[a-x, c, b],[c,b-x, a],[b, a, c-x]|=0

Solve the following determinant equation: |[x+a, b, c], [c, x+b, a], [a ,b, x+c]|=0

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c andb(a+c)> a c

Solve |(x+a,b,c),(a,x+b,c),(a,b,x+c)|=0

Solve the equation |{:(x+a,c+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0