5y(2y+1)3y(2y-1)=

Solution for 5y(2y+1)3y(2y-1)= equation:

Simplifying
5y(2y + 1) * 3y(2y + -1) = 0

Reorder the terms:
5y(1 + 2y) * 3y(2y + -1) = 0

Reorder the terms:
5y(1 + 2y) * 3y(-1 + 2y) = 0

Reorder the terms for easier multiplication:
5 * 3y * y(1 + 2y)(-1 + 2y) = 0

Multiply 5 * 3
15y * y(1 + 2y)(-1 + 2y) = 0

Multiply y * y
15y2(1 + 2y)(-1 + 2y) = 0

Multiply (1 + 2y) * (-1 + 2y)
15y2(1(-1 + 2y) + 2y * (-1 + 2y)) = 0
15y2((-1 * 1 + 2y * 1) + 2y * (-1 + 2y)) = 0
15y2((-1 + 2y) + 2y * (-1 + 2y)) = 0
15y2(-1 + 2y + (-1 * 2y + 2y * 2y)) = 0
15y2(-1 + 2y + (-2y + 4y2)) = 0

Combine like terms: 2y + -2y = 0
15y2(-1 + 0 + 4y2) = 0
15y2(-1 + 4y2) = 0
(-1 * 15y2 + 4y2 * 15y2) = 0
(-15y2 + 60y4) = 0

Solving
-15y2 + 60y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '15y2'.
15y2(-1 + 4y2) = 0

Factor a difference between two squares.
15y2((1 + 2y)(-1 + 2y)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 3
Set the factor '(-1 + 2y)' equal to zero and attempt to solve:

Simplifying
-1 + 2y = 0

Solving
-1 + 2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2y = 0 + 1
2y = 0 + 1

Combine like terms: 0 + 1 = 1
2y = 1

Divide each side by '2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0, -0.5, 0.5}