2X+1=X(X+1)-11

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Solution for 2X+1=X(X+1)-11 equation: 


Simplifying
2X + 1 = X(X + 1) + -11

Reorder the terms:
1 + 2X = X(X + 1) + -11

Reorder the terms:
1 + 2X = X(1 + X) + -11
1 + 2X = (1 * X + X * X) + -11
1 + 2X = (1X + X2) + -11

Reorder the terms:
1 + 2X = -11 + 1X + X2

Solving
1 + 2X = -11 + 1X + X2

Solving for variable 'X'.

Reorder the terms:
1 + 11 + 2X + -1X + -1X2 = -11 + 1X + X2 + 11 + -1X + -1X2

Combine like terms: 1 + 11 = 12
12 + 2X + -1X + -1X2 = -11 + 1X + X2 + 11 + -1X + -1X2

Combine like terms: 2X + -1X = 1X
12 + 1X + -1X2 = -11 + 1X + X2 + 11 + -1X + -1X2

Reorder the terms:
12 + 1X + -1X2 = -11 + 11 + 1X + -1X + X2 + -1X2

Combine like terms: -11 + 11 = 0
12 + 1X + -1X2 = 0 + 1X + -1X + X2 + -1X2
12 + 1X + -1X2 = 1X + -1X + X2 + -1X2

Combine like terms: 1X + -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}

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