x^2+10x+21=-2x+1

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Solution for x^2+10x+21=-2x+1 equation: 


Simplifying
x2 + 10x + 21 = -2x + 1

Reorder the terms:
21 + 10x + x2 = -2x + 1

Reorder the terms:
21 + 10x + x2 = 1 + -2x

Solving
21 + 10x + x2 = 1 + -2x

Solving for variable 'x'.

Reorder the terms:
21 + -1 + 10x + 2x + x2 = 1 + -2x + -1 + 2x

Combine like terms: 21 + -1 = 20
20 + 10x + 2x + x2 = 1 + -2x + -1 + 2x

Combine like terms: 10x + 2x = 12x
20 + 12x + x2 = 1 + -2x + -1 + 2x

Reorder the terms:
20 + 12x + x2 = 1 + -1 + -2x + 2x

Combine like terms: 1 + -1 = 0
20 + 12x + x2 = 0 + -2x + 2x
20 + 12x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 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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