Solve 2*(n+2)*(n-2)=64

$$2 \cdot ( n + 2 ) \cdot ( n - 2 ) = 64$$

Solve for n

$$n=-6$$

$$n=6$$

Steps by Finding Square Root

Use the distributive property to multiply 2 by n+2.

$$\left(2n+4\right)\left(n-2\right)=64$$

Use the distributive property to multiply 2n+4 by n-2 and combine like terms.

$$2n^{2}-8=64$$

Add 8 to both sides.

$$2n^{2}=64+8$$

Add 64 and 8 to get 72.

$$2n^{2}=72$$

Divide both sides by 2.

$$n^{2}=\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$n^{2}=36$$

Take the square root of both sides of the equation.

$$n=6 n=-6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by n+2.

$$\left(2n+4\right)\left(n-2\right)=64$$

Use the distributive property to multiply 2n+4 by n-2 and combine like terms.

$$2n^{2}-8=64$$

Subtract 64 from both sides.

$$2n^{2}-8-64=0$$

Subtract 64 from -8 to get -72.

$$2n^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 2\left(-72\right)}}{2\times 2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 2\left(-72\right)}}{2\times 2}$$

Multiply -4 times 2.

$$n=\frac{0±\sqrt{-8\left(-72\right)}}{2\times 2}$$

Multiply -8 times -72.

$$n=\frac{0±\sqrt{576}}{2\times 2}$$

Take the square root of 576.

$$n=\frac{0±24}{2\times 2}$$

Multiply 2 times 2.

$$n=\frac{0±24}{4}$$

Now solve the equation n=\frac{0±24}{4} when ± is plus. Divide 24 by 4.

$$n=6$$

Now solve the equation n=\frac{0±24}{4} when ± is minus. Divide -24 by 4.

$$n=-6$$

The equation is now solved.

$$n=6 n=-6$$