x^2+5x+22=-7x+2

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Solution for x^2+5x+22=-7x+2 equation: 


Simplifying
x2 + 5x + 22 = -7x + 2

Reorder the terms:
22 + 5x + x2 = -7x + 2

Reorder the terms:
22 + 5x + x2 = 2 + -7x

Solving
22 + 5x + x2 = 2 + -7x

Solving for variable 'x'.

Reorder the terms:
22 + -2 + 5x + 7x + x2 = 2 + -7x + -2 + 7x

Combine like terms: 22 + -2 = 20
20 + 5x + 7x + x2 = 2 + -7x + -2 + 7x

Combine like terms: 5x + 7x = 12x
20 + 12x + x2 = 2 + -7x + -2 + 7x

Reorder the terms:
20 + 12x + x2 = 2 + -2 + -7x + 7x

Combine like terms: 2 + -2 = 0
20 + 12x + x2 = 0 + -7x + 7x
20 + 12x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
20 + 12x + x2 = 0

Factor a trinomial.
(10 + x)(2 + x) = 0


Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {-10, -2}

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