x^2+2x=x+56

Solution for x^2+2x=x+56 equation:

Simplifying
x2 + 2x = x + 56

Reorder the terms:
2x + x2 = x + 56

Reorder the terms:
2x + x2 = 56 + x

Solving
2x + x2 = 56 + x

Solving for variable 'x'.

Reorder the terms:
-56 + 2x + -1x + x2 = 56 + x + -56 + -1x

Combine like terms: 2x + -1x = 1x
-56 + 1x + x2 = 56 + x + -56 + -1x

Reorder the terms:
-56 + 1x + x2 = 56 + -56 + x + -1x

Combine like terms: 56 + -56 = 0
-56 + 1x + x2 = 0 + x + -1x
-56 + 1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-56 + 1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-8, 7}