12y(y-3)=15y

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Solution for 12y(y-3)=15y equation: 


Simplifying
12y(y + -3) = 15y

Reorder the terms:
12y(-3 + y) = 15y
(-3 * 12y + y * 12y) = 15y
(-36y + 12y2) = 15y

Solving
-36y + 12y2 = 15y

Solving for variable 'y'.

Reorder the terms:
-36y + -15y + 12y2 = 15y + -15y

Combine like terms: -36y + -15y = -51y
-51y + 12y2 = 15y + -15y

Combine like terms: 15y + -15y = 0
-51y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-17 + 4y) = 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 '(-17 + 4y)' equal to zero and attempt to solve:

Simplifying
-17 + 4y = 0

Solving
-17 + 4y = 0

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

Add '17' to each side of the equation.
-17 + 17 + 4y = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 4y = 0 + 17
4y = 0 + 17

Combine like terms: 0 + 17 = 17
4y = 17

Divide each side by '4'.
y = 4.25

Simplifying
y = 4.25
Solution
y = {0, 4.25}

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