Solve (3n)^2-(-2)-sqrt{100}=(3n-2)^2

$$( 3 n ) ^ { 2 } - ( - 2 ) - \sqrt { 100 } = ( 3 n - 2 ) ^ { 2 }$$

Solve for n

$$n=1$$

Steps for Solving Linear Equation

Expand \left(3n\right)^{2}.

$$3^{2}n^{2}-\left(-2\right)-\sqrt{100}=\left(3n-2\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9n^{2}-\left(-2\right)-\sqrt{100}=\left(3n-2\right)^{2}$$

The opposite of -2 is 2.

$$9n^{2}+2-\sqrt{100}=\left(3n-2\right)^{2}$$

Calculate the square root of 100 and get 10.

$$9n^{2}+2-10=\left(3n-2\right)^{2}$$

Subtract 10 from 2 to get -8.

$$9n^{2}-8=\left(3n-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3n-2\right)^{2}.

$$9n^{2}-8=9n^{2}-12n+4$$

Subtract 9n^{2} from both sides.

$$9n^{2}-8-9n^{2}=-12n+4$$

Combine 9n^{2} and -9n^{2} to get 0.

$$-8=-12n+4$$

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

$$-12n+4=-8$$

Subtract 4 from both sides.

$$-12n=-8-4$$

Subtract 4 from -8 to get -12.

$$-12n=-12$$

Divide both sides by -12.

$$n=\frac{-12}{-12}$$

Divide -12 by -12 to get 1.

$$n=1$$