Simplify the expression: $|5x^2-10x+3|$

Step 1 ：Step 1: Factor the polynomial inside the absolute value. Here we have $|5x^2-10x+3|=|5(x^2-2x)+3|$

Step 2 ：Step 2: Complete the square inside the absolute value. $|5(x^2-2x)+3|=|5[(x-1{)}^2-1]+3|=|5(x-1{)}^2-5+3|=|5(x-1{)}^2-2|$

Step 3 ：Step 3: An absolute value is always positive, so we have $|5(x-1{)}^2-2|\ge 0$. This means the expression is equal to itself when $5(x-1{)}^2-2\ge 0$ and equal to its opposite when $5(x-1{)}^2-2<0$.

Step 4 ：Step 4: Solve for x in each case. If $5(x-1{)}^2-2\ge 0$, then $x\le 1-\sqrt{2/5}$ or $x\ge 1+\sqrt{2/5}$. If $5(x-1{)}^2-2<0$, then $1-\sqrt{2/5}<x<1+\sqrt{2/5}$. So the simplified expression is $5(x-1{)}^2-2$ when $x\le 1-\sqrt{2/5}$ or $x\ge 1+\sqrt{2/5}$, and $-5(x-1{)}^2+2$ when $1-\sqrt{2/5}<x<1+\sqrt{2/5}$.