x^2+21x+27=8x+5

Solution for x^2+21x+27=8x+5 equation:

Simplifying
x2 + 21x + 27 = 8x + 5

Reorder the terms:
27 + 21x + x2 = 8x + 5

Reorder the terms:
27 + 21x + x2 = 5 + 8x

Solving
27 + 21x + x2 = 5 + 8x

Solving for variable 'x'.

Reorder the terms:
27 + -5 + 21x + -8x + x2 = 5 + 8x + -5 + -8x

Combine like terms: 27 + -5 = 22
22 + 21x + -8x + x2 = 5 + 8x + -5 + -8x

Combine like terms: 21x + -8x = 13x
22 + 13x + x2 = 5 + 8x + -5 + -8x

Reorder the terms:
22 + 13x + x2 = 5 + -5 + 8x + -8x

Combine like terms: 5 + -5 = 0
22 + 13x + x2 = 0 + 8x + -8x
22 + 13x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
22 + 13x + x2 = 0

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

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
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 = {-11, -2}