a) x^2-7x+6=0 b) a^2+3a-18=0 C) 2y^2-6y-20=0 d) 4y^2+8y+3=0 e) 7x^2-21x=0 f) a^2-2a-9=0

a) $x^{2}-7x+6=0$<br />Factor the quadratic equation:<br />$(x-6)(x-1)=0$<br />Set each factor to zero and solve for x:<br />$x-6=0 \Rightarrow x=6$<br />$x-1=0 \Rightarrow x=1$<br /><br />b) $a^{2}+3a-18=0$<br />Factor the quadratic equation:<br />$(a+6)(a-3)=0$<br />Set each factor to zero and solve for a:<br />$a+6=0 \Rightarrow a=-6$<br />$a-3=0 \Rightarrow a=3$<br /><br />c) $2y^{2}-6y-20=0$<br />Factor the quadratic equation:<br />$2(y+2)(y-5)=0$<br />Set each factor to zero and solve for y:<br />$y+2=0 \Rightarrow y=-2$<br />$y-5=0 \Rightarrow y=5$<br /><br />d) $4y^{2}+8y+3=0$<br />Factor the quadratic equation:<br />$(2y+1)(2y+3)=0$<br />Set each factor to zero and solve for y:<br />$2y+1=0 \Rightarrow y=-\frac{1}{2}$<br />$2y+3=0 \Rightarrow y=-\frac{3}{2}$<br /><br />e) $7x^{2}-21x=0$<br />Factor out x:<br />$x(7x-21)=0$<br />Set each factor to zero and solve for x:<br />$x=0$<br />$7x-21=0 \Rightarrow 7x=21 \Rightarrow x=3$<br /><br />f) $a^{2}-2a-9=0$<br />Factor the quadratic equation:<br />$(a-3)(a+3)=0$<br />Set each factor to zero and solve for a:<br />$a-3=0 \Rightarrow a=3$<br />$a+3=0 \Rightarrow a=-3$