x^2+5x+10=-2x-2

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Solution for x^2+5x+10=-2x-2 equation: 


Simplifying
x2 + 5x + 10 = -2x + -2

Reorder the terms:
10 + 5x + x2 = -2x + -2

Reorder the terms:
10 + 5x + x2 = -2 + -2x

Solving
10 + 5x + x2 = -2 + -2x

Solving for variable 'x'.

Reorder the terms:
10 + 2 + 5x + 2x + x2 = -2 + -2x + 2 + 2x

Combine like terms: 10 + 2 = 12
12 + 5x + 2x + x2 = -2 + -2x + 2 + 2x

Combine like terms: 5x + 2x = 7x
12 + 7x + x2 = -2 + -2x + 2 + 2x

Reorder the terms:
12 + 7x + x2 = -2 + 2 + -2x + 2x

Combine like terms: -2 + 2 = 0
12 + 7x + x2 = 0 + -2x + 2x
12 + 7x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}

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