Solve for n 3n^2+8n+16=2n^2

$3 n^{2} + 8 n + 16 = 2 n^{2}$

Move all terms containing $n$ to the left side of the equation.

Subtract $2 n^{2}$ from both sides of the equation.

$3 n^{2} + 8 n + 16 - 2 n^{2} = 0$

Subtract $2 n^{2}$ from $3 n^{2}$ .

$n^{2} + 8 n + 16 = 0$

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$n^{2} + 8 n + 4^{2} = 0$

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

$8 n = 2 \cdot n \cdot 4$

Rewrite the polynomial.

$n^{2} + 2 \cdot n \cdot 4 + 4^{2} = 0$

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

${(n + 4)}^{2} = 0$

Set the $n + 4$ equal to $0$ .

$n + 4 = 0$

Subtract $4$ from both sides of the equation.

$n = - 4$