Solve (2n-1)2n=-2*a

$$( 2 n - 1 ) 2 n = - 2 \times a$$

Solve for a

$$a=n\left(1-2n\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2n-1 by 2.

$$\left(4n-2\right)n=-2a$$

Use the distributive property to multiply 4n-2 by n.

$$4n^{2}-2n=-2a$$

Swap sides so that all variable terms are on the left hand side.

$$-2a=4n^{2}-2n$$

Divide both sides by -2.

$$\frac{-2a}{-2}=\frac{2n\left(2n-1\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$a=\frac{2n\left(2n-1\right)}{-2}$$

Divide 2n\left(-1+2n\right) by -2.

$$a=n-2n^{2}$$

Solve for n

$$n=\frac{\sqrt{1-8a}+1}{4}$$

$$n=\frac{-\sqrt{1-8a}+1}{4}\text{, }a\leq \frac{1}{8}$$