y^2+21=3y^2-51

Solution for y^2+21=3y^2-51 equation:

Simplifying
y2 + 21 = 3y2 + -51

Reorder the terms:
21 + y2 = 3y2 + -51

Reorder the terms:
21 + y2 = -51 + 3y2

Solving
21 + y2 = -51 + 3y2

Solving for variable 'y'.

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

Add '-3y2' to each side of the equation.
21 + y2 + -3y2 = -51 + 3y2 + -3y2

Combine like terms: y2 + -3y2 = -2y2
21 + -2y2 = -51 + 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
21 + -2y2 = -51 + 0
21 + -2y2 = -51

Add '-21' to each side of the equation.
21 + -21 + -2y2 = -51 + -21

Combine like terms: 21 + -21 = 0
0 + -2y2 = -51 + -21
-2y2 = -51 + -21

Combine like terms: -51 + -21 = -72
-2y2 = -72

Divide each side by '-2'.
y2 = 36

Simplifying
y2 = 36

Take the square root of each side:
y = {-6, 6}