Solve: (x2 + x) (x2 + x – 2 ) = 24

Answer:
Let (x2 + x) = m
∴ m(m – 2) = 24
∴ m2 – 2m = 24
∴ m2  - 2m  - 24 = 0
∴ m2 – 6m + 4m – 24 = 0
∴ m(m – 6) + 4( m – 6 ) = 0
∴ (m – 6) (m + 4 ) = 0
∴ m – 6 = 0	∴ m + 4 = 0
∴ m = 6	∴ m = - 4
Re substituting  m = (x2 + x)
∴ x2 + x = 6	∴ x2 + x = - 4
∴ x2 + x – 6 = 0	∴ x 2 + x + 4 = 0
∴ x2 + 3x – 2x – 6 = 0	Here, a = 1 , b = 1, c = 4
∴ x(x + 3) – 2(x + 3) = 0	∴ b2 – 4ac = 12 – 4 (1) (4)
∴ (x + 3 ) ( x – 2 ) = 0	∴ b2 – 4ac = - 15
∴ x + 3 = 0   OR  x – 2 = 0	∴ b2 – 4ac < 0
∴ x = - 3   OR   x  = 2	∴ the roots are not real but imaginary numbers
	∴ we can avoid this equation