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

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

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

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

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

Multiply (-6 + 2y) * (3 + 2y)
(-6(3 + 2y) + 2y * (3 + 2y)) = 0
((3 * -6 + 2y * -6) + 2y * (3 + 2y)) = 0
((-18 + -12y) + 2y * (3 + 2y)) = 0
(-18 + -12y + (3 * 2y + 2y * 2y)) = 0
(-18 + -12y + (6y + 4y2)) = 0

Combine like terms: -12y + 6y = -6y
(-18 + -6y + 4y2) = 0

Solving
-18 + -6y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -3y + 2y2) = 0

Factor a trinomial.
2((-3 + -2y)(3 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1.5, 3}