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

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


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

Reorder the terms:
2y(-5 + 3y) = 3(y + 5)
(-5 * 2y + 3y * 2y) = 3(y + 5)
(-10y + 6y2) = 3(y + 5)

Reorder the terms:
-10y + 6y2 = 3(5 + y)
-10y + 6y2 = (5 * 3 + y * 3)
-10y + 6y2 = (15 + 3y)

Solving
-10y + 6y2 = 15 + 3y

Solving for variable 'y'.

Reorder the terms:
-15 + -10y + -3y + 6y2 = 15 + 3y + -15 + -3y

Combine like terms: -10y + -3y = -13y
-15 + -13y + 6y2 = 15 + 3y + -15 + -3y

Reorder the terms:
-15 + -13y + 6y2 = 15 + -15 + 3y + -3y

Combine like terms: 15 + -15 = 0
-15 + -13y + 6y2 = 0 + 3y + -3y
-15 + -13y + 6y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-15 + -13y + 6y2 = 0

Factor a trinomial.
(-5 + -6y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-5 + -6y)' equal to zero and attempt to solve:

Simplifying
-5 + -6y = 0

Solving
-5 + -6y = 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 + -6y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6y = 0 + 5
-6y = 0 + 5

Combine like terms: 0 + 5 = 5
-6y = 5

Divide each side by '-6'.
y = -0.8333333333

Simplifying
y = -0.8333333333

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.8333333333, 3}

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