first multiple both sides by 4 = 12k^2+29k-1000, rewrite it 12k^2+125k-96k-1000=0, factor k out from the expression k x (12k+125)-96k-1000=0, then factor out 8 k x (12k+125)-8(12k+125)=0, factor out 12k+125 to (12k+125)x(k-8)=0, now when the product of factors equals 0, at least one factor is 0 - 12k+125=0 k-8=0, solve the equation for k k=-125/12
k=8
