(y+3)(y+10)=-10

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Solution for (y+3)(y+10)=-10 equation: 


Simplifying
(y + 3)(y + 10) = -10

Reorder the terms:
(3 + y)(y + 10) = -10

Reorder the terms:
(3 + y)(10 + y) = -10

Multiply (3 + y) * (10 + y)
(3(10 + y) + y(10 + y)) = -10
((10 * 3 + y * 3) + y(10 + y)) = -10
((30 + 3y) + y(10 + y)) = -10
(30 + 3y + (10 * y + y * y)) = -10
(30 + 3y + (10y + y2)) = -10

Combine like terms: 3y + 10y = 13y
(30 + 13y + y2) = -10

Solving
30 + 13y + y2 = -10

Solving for variable 'y'.

Reorder the terms:
30 + 10 + 13y + y2 = -10 + 10

Combine like terms: 30 + 10 = 40
40 + 13y + y2 = -10 + 10

Combine like terms: -10 + 10 = 0
40 + 13y + y2 = 0

Factor a trinomial.
(8 + y)(5 + y) = 0


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

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

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5
Solution
y = {-8, -5}

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