Find the real solutions of each equation 5x 62 5x 6 6 0

Find the real solutions of each equation. (5x + 6)^2 - (5x + 6) - 6 = 0 x^4 - 7x^2 + 12 = 0

1) (5x +6)^2 - (5x +6) -6 =0

let 5x +6 =y

So, y^2 -y -6 =0

y^2 -3y +2y -6 =0

y(y -3) +2(y-3) =0

(y +2)(y -3) =0

y = -2 ; 5x +6 = -2

x = 8/5

y =3 ; 5x +6 =3

x = -3/5

Solution : x = -3/5 , 8/5

2) x^4 -7x^2 +12 =0

to make it a quadratic: lets assume y = x^2

So, y^2 -7y +12 =0

y^2 -4y -4y +12 =0

y( y -4) -4( y-12) =0

(y-4)(y-12) =0

y = 4 ; x^2 =4

x = 2, -2

y =12 ; x^2 =12

x = 2sqrt3 , -2sqrt3

Solution: x = -2 , 2 , 2sqrt3 , -2sqrt3