x+7=x^2+5x+2

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


Simplifying
x + 7 = x2 + 5x + 2

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

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

Solving
7 + x = 2 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -2 + x + -5x + -1x2 = 2 + 5x + x2 + -2 + -5x + -1x2

Combine like terms: 7 + -2 = 5
5 + x + -5x + -1x2 = 2 + 5x + x2 + -2 + -5x + -1x2

Combine like terms: x + -5x = -4x
5 + -4x + -1x2 = 2 + 5x + x2 + -2 + -5x + -1x2

Reorder the terms:
5 + -4x + -1x2 = 2 + -2 + 5x + -5x + x2 + -1x2

Combine like terms: 2 + -2 = 0
5 + -4x + -1x2 = 0 + 5x + -5x + x2 + -1x2
5 + -4x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
5 + -4x + -1x2 = 0 + x2 + -1x2
5 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + -4x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(5 + x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {1, -5}

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