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

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


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

Reorder the terms:
5y(2 + 3y) = -3y + -2
(2 * 5y + 3y * 5y) = -3y + -2
(10y + 15y2) = -3y + -2

Reorder the terms:
10y + 15y2 = -2 + -3y

Solving
10y + 15y2 = -2 + -3y

Solving for variable 'y'.

Reorder the terms:
2 + 10y + 3y + 15y2 = -2 + -3y + 2 + 3y

Combine like terms: 10y + 3y = 13y
2 + 13y + 15y2 = -2 + -3y + 2 + 3y

Reorder the terms:
2 + 13y + 15y2 = -2 + 2 + -3y + 3y

Combine like terms: -2 + 2 = 0
2 + 13y + 15y2 = 0 + -3y + 3y
2 + 13y + 15y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
2 + 13y + 15y2 = 0

Factor a trinomial.
(2 + 3y)(1 + 5y) = 0


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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667

Subproblem 2
Set the factor '(1 + 5y)' equal to zero and attempt to solve:

Simplifying
1 + 5y = 0

Solving
1 + 5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {-0.6666666667, -0.2}

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