y^2+(5y)=-10-2y^2-6y

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Solution for y^2+(5y)=-10-2y^2-6y equation: 


Simplifying
y2 + (5y) = -10 + -2y2 + -6y

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

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

Solving
(5y) + y2 = -10 + -6y + -2y2

Solving for variable 'y'.

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

Combine like terms: (5y) + 6y = 11y
10 + 11y + y2 + 2y2 = -10 + -6y + -2y2 + 10 + 6y + 2y2

Combine like terms: y2 + 2y2 = 3y2
10 + 11y + 3y2 = -10 + -6y + -2y2 + 10 + 6y + 2y2

Reorder the terms:
10 + 11y + 3y2 = -10 + 10 + -6y + 6y + -2y2 + 2y2

Combine like terms: -10 + 10 = 0
10 + 11y + 3y2 = 0 + -6y + 6y + -2y2 + 2y2
10 + 11y + 3y2 = -6y + 6y + -2y2 + 2y2

Combine like terms: -6y + 6y = 0
10 + 11y + 3y2 = 0 + -2y2 + 2y2
10 + 11y + 3y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
10 + 11y + 3y2 = 0

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


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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

Simplifying
y = -2

Subproblem 2
Set the factor '(5 + 3y)' equal to zero and attempt to solve:

Simplifying
5 + 3y = 0

Solving
5 + 3y = 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 + 3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3y = 0 + -5
3y = 0 + -5

Combine like terms: 0 + -5 = -5
3y = -5

Divide each side by '3'.
y = -1.666666667

Simplifying
y = -1.666666667
Solution
y = {-2, -1.666666667}

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