2x+1=x^2+x-11

Solution for 2x+1=x^2+x-11 equation:

Simplifying
2x + 1 = x2 + x + -11

Reorder the terms:
1 + 2x = x2 + x + -11

Reorder the terms:
1 + 2x = -11 + x + x2

Solving
1 + 2x = -11 + x + x2

Solving for variable 'x'.

Reorder the terms:
1 + 11 + 2x + -1x + -1x2 = -11 + x + x2 + 11 + -1x + -1x2

Combine like terms: 1 + 11 = 12
12 + 2x + -1x + -1x2 = -11 + x + x2 + 11 + -1x + -1x2

Combine like terms: 2x + -1x = 1x
12 + 1x + -1x2 = -11 + x + x2 + 11 + -1x + -1x2

Reorder the terms:
12 + 1x + -1x2 = -11 + 11 + x + -1x + x2 + -1x2

Combine like terms: -11 + 11 = 0
12 + 1x + -1x2 = 0 + x + -1x + x2 + -1x2
12 + 1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
12 + 1x + -1x2 = 0 + x2 + -1x2
12 + 1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 1x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {4, -3}