(y-3)(2y+6)=0

Solution for (y-3)(2y+6)=0 equation:

Simplifying
(y + -3)(2y + 6) = 0

Reorder the terms:
(-3 + y)(2y + 6) = 0

Reorder the terms:
(-3 + y)(6 + 2y) = 0

Multiply (-3 + y) * (6 + 2y)
(-3(6 + 2y) + y(6 + 2y)) = 0
((6 * -3 + 2y * -3) + y(6 + 2y)) = 0
((-18 + -6y) + y(6 + 2y)) = 0
(-18 + -6y + (6 * y + 2y * y)) = 0
(-18 + -6y + (6y + 2y2)) = 0

Combine like terms: -6y + 6y = 0
(-18 + 0 + 2y2) = 0
(-18 + 2y2) = 0

Solving
-18 + 2y2 = 0

Solving for variable 'y'.

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

Add '18' to each side of the equation.
-18 + 18 + 2y2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 2y2 = 0 + 18
2y2 = 0 + 18

Combine like terms: 0 + 18 = 18
2y2 = 18

Divide each side by '2'.
y2 = 9

Simplifying
y2 = 9

Take the square root of each side:
y = {-3, 3}