-x+7=x^2+2x+9

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Solution for -x+7=x^2+2x+9 equation: 


Simplifying
-1x + 7 = x2 + 2x + 9

Reorder the terms:
7 + -1x = x2 + 2x + 9

Reorder the terms:
7 + -1x = 9 + 2x + x2

Solving
7 + -1x = 9 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -9 + -1x + -2x + -1x2 = 9 + 2x + x2 + -9 + -2x + -1x2

Combine like terms: 7 + -9 = -2
-2 + -1x + -2x + -1x2 = 9 + 2x + x2 + -9 + -2x + -1x2

Combine like terms: -1x + -2x = -3x
-2 + -3x + -1x2 = 9 + 2x + x2 + -9 + -2x + -1x2

Reorder the terms:
-2 + -3x + -1x2 = 9 + -9 + 2x + -2x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-2 + -3x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-2 + -3x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-2 + -3x + -1x2 = 0 + x2 + -1x2
-2 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 3x + x2) = 0

Factor a trinomial.
-1((2 + x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-2, -1}

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