Solve by Factoring 16x^2-24x+13=4

$16 x^{2} - 24 x + 13 = 4$

Subtract $4$ from both sides of the equation.

$16 x^{2} - 24 x + 13 - 4 = 0$

Subtract $4$ from $13$ .

$16 x^{2} - 24 x + 9 = 0$

Factor using the perfect square rule.

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

${(4 x)}^{2} - 24 x + 9 = 0$

Rewrite $9$ as $3^{2}$ .

${(4 x)}^{2} - 24 x + 3^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$24 x = 2 \cdot (4 x) \cdot 3$

Rewrite the polynomial.

${(4 x)}^{2} - 2 \cdot (4 x) \cdot 3 + 3^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 4 x$ and $b = 3$ .

${(4 x - 3)}^{2} = 0$

Set the $4 x - 3$ equal to $0$ .

$4 x - 3 = 0$

Solve for $x$ .

Add $3$ to both sides of the equation.

$4 x = 3$

Divide each term in $4 x = 3$ by $4$ and simplify.

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$