Help me on quadratics

Question

27x-54(x-2)=9x^2-18x

4r^3+4r^2=9(r+1)

help me I am stuck

Answer 1

(1) 27x-54(x-2) = 9x²-18x

27x-54x+108 = 9x²-18x

Move the left side of the equation to the right and change the sign.

0 = 9x²-18x - 27x+54x-108

combine like terms.

0 = 9x²+9x-108

Factor out 9

0 = 9( x²+x-12 )

Divide 9 both side:

0 = x²+x-12

Factor:

0 = (x+4) (x-3)

x=-4 or x =3

(1) 4r³+4r²=9(r+1)

Factor the left side and move the right side to the left.

4r²(r+1)-9(r+1)=0

(4r²-9)(r+1) = 0

Split into 2 equations (you got 3 solutions for r):

4r²-9 = 0 r+1 = 0

4r² = 9 r= -1

r² = 9/4

r = ± 3/2