Question 1121866
<pre>
Use formula for the left side of the equation:

{{{matrix(1,3,
abs(matrix(3,3,A,B,C,D,E,F,G,H,I)),
""="",
A*E*I+B*F*G+C*D*H-C*E*G-B*D*I-A*F*H)}}}

{{{matrix(1,3,
abs(matrix(3,3,K,3+K,-10,1-K,2-K,5,2,4+K,-K)),
""="",
K*(2-K)*(-K)+(3+K)*(5)*(2)+(-10)*(1-K)*(4+K)-(-10)*(2-K)*(2)-(3+K)*(1-K)*(-K)-K*(5)*(4+K))}}}

That simplifies to:

{{{K^2 + 3 K + 30}}} = left side of equation:

So the equation is:

{{{matrix(1,3,K^2 + 3 K + 30,""="",48)}}}

Get 0 on the right by subtracting 48 from both sides

{{{matrix(1,3,K^2 + 3 K - 18,""="",0)}}}

Factor left side:

{{{matrix(1,3,(K + 6)(K - 3),""="",0)}}} 

Use zero-factor principle:

K+6 = 0;  K-3 = 0
  K = -6;   K = 3   <---two solutions!

Edwin</pre>