x^2+7x=27+x

Solution for x^2+7x=27+x equation:

Simplifying
x2 + 7x = 27 + x

Reorder the terms:
7x + x2 = 27 + x

Solving
7x + x2 = 27 + x

Solving for variable 'x'.

Reorder the terms:
-27 + 7x + -1x + x2 = 27 + x + -27 + -1x

Combine like terms: 7x + -1x = 6x
-27 + 6x + x2 = 27 + x + -27 + -1x

Reorder the terms:
-27 + 6x + x2 = 27 + -27 + x + -1x

Combine like terms: 27 + -27 = 0
-27 + 6x + x2 = 0 + x + -1x
-27 + 6x + x2 = x + -1x

Combine like terms: x + -1x = 0
-27 + 6x + x2 = 0

Factor a trinomial.
(-9 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

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

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

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-9, 3}