x+3=x^2+10x+23

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Solution for x+3=x^2+10x+23 equation: 


Simplifying
x + 3 = x2 + 10x + 23

Reorder the terms:
3 + x = x2 + 10x + 23

Reorder the terms:
3 + x = 23 + 10x + x2

Solving
3 + x = 23 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
3 + -23 + x + -10x + -1x2 = 23 + 10x + x2 + -23 + -10x + -1x2

Combine like terms: 3 + -23 = -20
-20 + x + -10x + -1x2 = 23 + 10x + x2 + -23 + -10x + -1x2

Combine like terms: x + -10x = -9x
-20 + -9x + -1x2 = 23 + 10x + x2 + -23 + -10x + -1x2

Reorder the terms:
-20 + -9x + -1x2 = 23 + -23 + 10x + -10x + x2 + -1x2

Combine like terms: 23 + -23 = 0
-20 + -9x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-20 + -9x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-20 + -9x + -1x2 = 0 + x2 + -1x2
-20 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 9x + x2) = 0

Factor a trinomial.
-1((5 + x)(4 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-5, -4}

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