9y(y+5)=2y(3)

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Solution for 9y(y+5)=2y(3) equation: 


Simplifying
9y(y + 5) = 2y(3)

Reorder the terms:
9y(5 + y) = 2y(3)
(5 * 9y + y * 9y) = 2y(3)
(45y + 9y2) = 2y(3)

Reorder the terms for easier multiplication:
45y + 9y2 = 2 * 3y

Multiply 2 * 3
45y + 9y2 = 6y

Solving
45y + 9y2 = 6y

Solving for variable 'y'.

Reorder the terms:
45y + -6y + 9y2 = 6y + -6y

Combine like terms: 45y + -6y = 39y
39y + 9y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
39y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(13 + 3y) = 0

Ignore the factor 3.

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 '(13 + 3y)' equal to zero and attempt to solve:

Simplifying
13 + 3y = 0

Solving
13 + 3y = 0

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

Add '-13' to each side of the equation.
13 + -13 + 3y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 3y = 0 + -13
3y = 0 + -13

Combine like terms: 0 + -13 = -13
3y = -13

Divide each side by '3'.
y = -4.333333333

Simplifying
y = -4.333333333
Solution
y = {0, -4.333333333}

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