QUADRATIC EQUATION RECTANGLE PROBLEM

a rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4cm. The length of the rectangular carpet is 2m less than three times its width. FInd the dimensions of the rectangular carpet.

plzz explain the solution step by step and accurately

thanks

Side of square carpet = 4 m ( NOT 4 cm)

Area of square carpet = 4 X 4 = 16 m^2

Area of rectangular carpet is also 16 m^2

Let the width of the rectangular carpet be x m

Length of the rectangular carpet will be 3x - 2 m

Area of rectangular carpet = ( 3x -2) x = 3x^2 -2x = 16

3x^2 - 2x - 16 = 0

3x^2 +6x -8x -16 = 0

3x ( x + 2) -8( x+2) = 0
( 3x - 8) ( x+2) = 0

x = 8/3 m

ANSWER Width = 8/3 m Length = 6m

CHECK

Area = 8/3 X 6 = 16 m^2