4y(y+3)=2y

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Solution for 4y(y+3)=2y equation: 


Simplifying
4y(y + 3) = 2y

Reorder the terms:
4y(3 + y) = 2y
(3 * 4y + y * 4y) = 2y
(12y + 4y2) = 2y

Solving
12y + 4y2 = 2y

Solving for variable 'y'.

Reorder the terms:
12y + -2y + 4y2 = 2y + -2y

Combine like terms: 12y + -2y = 10y
10y + 4y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
10y + 4y2 = 0

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

Ignore the factor 2.

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}

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