4n^2-75=n^2

Solution for 4n^2-75=n^2 equation:

Simplifying
4n2 + -75 = n2

Reorder the terms:
-75 + 4n2 = n2

Solving
-75 + 4n2 = n2

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1n2' to each side of the equation.
-75 + 4n2 + -1n2 = n2 + -1n2

Combine like terms: 4n2 + -1n2 = 3n2
-75 + 3n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-75 + 3n2 = 0

Add '75' to each side of the equation.
-75 + 75 + 3n2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 3n2 = 0 + 75
3n2 = 0 + 75

Combine like terms: 0 + 75 = 75
3n2 = 75

Divide each side by '3'.
n2 = 25

Simplifying
n2 = 25

Take the square root of each side:
n = {-5, 5}