a) x^2-x-3x+3=0
Combining like terms: x^2 - 4x + 3 = 0
Factoring: (x - 1)(x - 3) = 0
Setting each factor equal to zero:
x - 1 = 0 or x - 3 = 0
x = 1 or x = 3

b) x(x-3)=4x-12
Expanding: x^2 - 3x = 4x - 12
Combining like terms: x^2 - 7x + 12 = 0
Factoring: (x - 3)(x - 4) = 0
Setting each factor equal to zero:
x - 3 = 0 or x - 4 = 0
x = 3 or x = 4

c) x^3-4x-15x-30=0
Combining like terms: x^3 - 19x - 30 = 0
This equation does not factor easily, so we can use numerical methods or a graphing calculator to find the solutions. The solutions are approximately x = -2.35, x = 2.35, and x = 6.29.

d) x^3+27+(x+3)(x-9)=0
Expanding: x^3 + 27 + x^2 - 9x + 3x - 27 = 0
Combining like terms: x^3 + x^2 - 6x = 0
Factoring out an x: x(x^2 + x - 6) = 0
Factoring the quadratic: x(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x = 0 or x + 3 = 0 or x - 2 = 0
x = 0 or x = -3 or x = 2

e) 5x^3-7x^2-15x+21=0
This equation does not factor easily, so we can use numerical methods or a graphing calculator to find the solutions. The solutions are approximately x = -1.48, x = 1.48, and x = 1.19.

f) (x-3)^2=4x^2-20x+25
Expanding: x^2 - 6x + 9 = 4x^2 - 20x + 25
Combining like terms: 3x^2 - 14x + 16 = 0
This equation does not factor easily, so we can use numerical methods or a graphing calculator to find the solutions. The solutions are approximately x = 1.33 and x = 3.33.

g) x+x^2-x^3-x^4=0
This equation does not factor easily, so we can use numerical methods or a graphing calculator to find the solutions. The solutions are approximately x = -1.38, x = 0, x = 1, and x = -0.38.

h) 2x^3+3x^2+2x+3=0
This equation does not factor easily, so we can use numerical methods or a graphing calculator to find the solutions. The solutions are approximately x = -1.32, x = -0.34 + 0.79i, and x = -0.34 - 0.79i.