Help factorising??????

Hi, I need help with these question please explain thanks!

1) 5x^3-16x^2+12x
2) 48x-24x^2+3x^2
3) (x-1)^2+4(x-1)+3

1)

5x³ - 16x² + 12x
--> factor out x

x(5x² - 16x + 12x)
--> multiply 5 * 12 = 60, factor to find factors that add to 16

10*6 = 60 and 10 + 6 = 16
-->

5x² - 10x - 6x + 12 = 5x(x - 2) - 6(x - 2) = (5x - 6)(x - 2)
-->

5x³ - 16x² + 12x = x(5x - 6)(x - 2)

2) 48x - 24x² + 3x² = 48x - 21x²
--> factor out 3x

3x(16 - 7x²)

3) (x - 1)² + 4(x - 1) + 3
--> solve following problem

X² + 4X + 3 = (X + 1)(X + 3)
--> plug in X = (x - 1)

(x - 1 + 1)(x - 1 + 3) = x(x + 2)

1.) In order to find factors first we equate the equation to zero
5x^3 -16x^2+12x = 0

x( 5x^2 -16x +12)=0

for second order euation roots can be found by (-b (+ or -)sqr(b^2 -4ac))/(2a)
a=5, b=-16, c=12
after substitution we get two roots (16+4)/(2*5)=2 ; (16-4)/(2*5)=1.2
so the roots for the given equation are x=0; x=2 ; x= 1.2
2.)48x -24x^2 +3x^2

from the above 48x -21x^2=0
x(48-21x)=0
so the roots are : x=0 ; x=(48/21)
3.)(x-1)^2 +4(x-1)+3
expand the equation and equate it to zero
x^2 -2x+1 +4x-4+3=0

x^2+2x=0
x(x+2)=0
so the roots are x=0 and x=-2