(3y*3y)-(5*5)+(y*y)=25

Solution for (3y*3y)-(5*5)+(y*y)=25 equation:

Simplifying
(3y * 3y) + -1(5 * 5) + (y * y) = 25

Reorder the terms for easier multiplication:
(3 * 3y * y) + -1(5 * 5) + (y * y) = 25

Multiply 3 * 3
(9y * y) + -1(5 * 5) + (y * y) = 25

Multiply y * y
(9y2) + -1(5 * 5) + (y * y) = 25

Multiply 5 * 5
(9y2) + -1(25) + (y * y) = 25

Multiply -1 * 25
(9y2) + -25 + (y * y) = 25

Multiply y * y
(9y2) + -25 + (y2) = 25
(9y2) + -25 + y2 = 25

Reorder the terms:
-25 + (9y2) + y2 = 25

Combine like terms: (9y2) + y2 = 10y2
-25 + 10y2 = 25

Solving
-25 + 10y2 = 25

Solving for variable 'y'.

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

Add '25' to each side of the equation.
-25 + 25 + 10y2 = 25 + 25

Combine like terms: -25 + 25 = 0
0 + 10y2 = 25 + 25
10y2 = 25 + 25

Combine like terms: 25 + 25 = 50
10y2 = 50

Divide each side by '10'.
y2 = 5

Simplifying
y2 = 5

Take the square root of each side:
y = {-2.236067978, 2.236067978}