Use factoring to solve (3x – 2)(x + 4) = 24.

Answer 1

The equation is (3x - 2)(x + 4) = 24.

By foil method : (a + b)(c + d) = ac + ad + bc + bd.

3x^2 - 2x + 12x - 8 = 24

Subtract 24 from each side.

3x^2 - 2x + 12x - 8 - 24 = 0

3x^2  + 10x - 32 = 0

By factoring by grouping.

3x^2 - 6x + 16x - 32 = 0

3x(x - 2) + 16(x - 2) = 0

Factor : (x - 2)(3x + 16) = 0

Apply zero product property.

x - 2 = 0  and  3x + 16 = 0

x = 2  and  x = - 16/3.

The solutions are x = 2 and x = - 16/3.