5y(2y+3)(2y-3)=

Solution for 5y(2y+3)(2y-3)= equation:

Simplifying
5y(2y + 3)(2y + -3) = 0

Reorder the terms:
5y(3 + 2y)(2y + -3) = 0

Reorder the terms:
5y(3 + 2y)(-3 + 2y) = 0

Multiply (3 + 2y) * (-3 + 2y)
5y(3(-3 + 2y) + 2y * (-3 + 2y)) = 0
5y((-3 * 3 + 2y * 3) + 2y * (-3 + 2y)) = 0
5y((-9 + 6y) + 2y * (-3 + 2y)) = 0
5y(-9 + 6y + (-3 * 2y + 2y * 2y)) = 0
5y(-9 + 6y + (-6y + 4y2)) = 0

Combine like terms: 6y + -6y = 0
5y(-9 + 0 + 4y2) = 0
5y(-9 + 4y2) = 0
(-9 * 5y + 4y2 * 5y) = 0
(-45y + 20y3) = 0

Solving
-45y + 20y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-9 + 4y2) = 0

Factor a difference between two squares.
5y((3 + 2y)(-3 + 2y)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
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 3
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
Solution
y = {0, -1.5, 1.5}