8y(y-2)=4y

Solution for 8y(y-2)=4y equation:

Simplifying
8y(y + -2) = 4y

Reorder the terms:
8y(-2 + y) = 4y
(-2 * 8y + y * 8y) = 4y
(-16y + 8y2) = 4y

Solving
-16y + 8y2 = 4y

Solving for variable 'y'.

Reorder the terms:
-16y + -4y + 8y2 = 4y + -4y

Combine like terms: -16y + -4y = -20y
-20y + 8y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-20y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4y'.
4y(-5 + 2y) = 0

Ignore the factor 4.
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 '(-5 + 2y)' equal to zero and attempt to solve:

Simplifying
-5 + 2y = 0

Solving
-5 + 2y = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2y = 0 + 5
2y = 0 + 5

Combine like terms: 0 + 5 = 5
2y = 5

Divide each side by '2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {0, 2.5}