Write in Standard Form -3(2x-1)(2x+1)=2

$- 3 (2 x - 1) (2 x + 1) = 2$

Subtract $2$ from both sides of the equation.

$- 3 (2 x - 1) (2 x + 1) - 2 = 0$

Simplify $- 3 (2 x - 1) (2 x + 1) - 2$ .

Simplify each term.

Apply the distributive property.

$(- 3 (2 x) - 3 \cdot - 1) (2 x + 1) - 2 = 0$

Multiply $2$ by $- 3$ .

$(- 6 x - 3 \cdot - 1) (2 x + 1) - 2 = 0$

Multiply $- 3$ by $- 1$ .

$(- 6 x + 3) (2 x + 1) - 2 = 0$

Expand $(- 6 x + 3) (2 x + 1)$ using the FOIL Method.

Apply the distributive property.

$- 6 x (2 x + 1) + 3 (2 x + 1) - 2 = 0$

Apply the distributive property.

$- 6 x (2 x) - 6 x \cdot 1 + 3 (2 x + 1) - 2 = 0$

Apply the distributive property.

$- 6 x (2 x) - 6 x \cdot 1 + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 6 \cdot 2 x \cdot x - 6 x \cdot 1 + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 6 \cdot 2 (x \cdot x) - 6 x \cdot 1 + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Multiply $x$ by $x$ .

$- 6 \cdot 2 x^{2} - 6 x \cdot 1 + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Multiply $- 6$ by $2$ .

$- 12 x^{2} - 6 x \cdot 1 + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Multiply $- 6$ by $1$ .

$- 12 x^{2} - 6 x + 3 (2 x) + 3 \cdot 1 - 2 = 0$

Multiply $2$ by $3$ .

$- 12 x^{2} - 6 x + 6 x + 3 \cdot 1 - 2 = 0$

Multiply $3$ by $1$ .

$- 12 x^{2} - 6 x + 6 x + 3 - 2 = 0$

Add $- 6 x$ and $6 x$ .

$- 12 x^{2} + 0 + 3 - 2 = 0$

Add $- 12 x^{2}$ and $0$ .

$- 12 x^{2} + 3 - 2 = 0$

Subtract $2$ from $3$ .

$- 12 x^{2} + 1 = 0$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

The standard form is $- 12 x^{2} + 1$ .

$- 12 x^{2} + 1 = 0$