(a) Simplify $3x (4x–5)+3$ and find its values for 

(i) $x = 3$ 

(ii) $x =\frac{1}{2}$

(b) Simplify $a(a^2+a+1)+5$and find its value for 

(i) $a=0$, 

(ii) $a = 1$ 

(iii) $a=-1$.

(a) Consider the given expression $3x (4x–5)+3$.

Multiply the terms inside the parenthesis and simplify to get the following,

$3x (4x–5)+3=12x^2-15x+3$

(i) Substitute $x = 3$ in the above expression to get the following,

$12x^2-15x+3=12{\left(3\right)}^2-15\left(3\right)+3$

$=108-45+3$

$=66$

Hence, the value of the simplified expression is 66.

(i) Substitute $x =\frac{1}{2}$ in the above expression to get the following,

$12x^2-15x+3=12{\left(\frac{1}{2}\right)}^2-15\left(\frac{1}{2}\right)+3$

$=3-\frac{15}{2}+3$

$=-\frac{3}{2}$

Hence, the value of the simplified expression is $-\frac{3}{2}$.