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

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

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

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

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

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