4X+11=2X^2+13X+6

Solution for 4X+11=2X^2+13X+6 equation:

Simplifying
4X + 11 = 2X2 + 13X + 6

Reorder the terms:
11 + 4X = 2X2 + 13X + 6

Reorder the terms:
11 + 4X = 6 + 13X + 2X2

Solving
11 + 4X = 6 + 13X + 2X2

Solving for variable 'X'.

Reorder the terms:
11 + -6 + 4X + -13X + -2X2 = 6 + 13X + 2X2 + -6 + -13X + -2X2

Combine like terms: 11 + -6 = 5
5 + 4X + -13X + -2X2 = 6 + 13X + 2X2 + -6 + -13X + -2X2

Combine like terms: 4X + -13X = -9X
5 + -9X + -2X2 = 6 + 13X + 2X2 + -6 + -13X + -2X2

Reorder the terms:
5 + -9X + -2X2 = 6 + -6 + 13X + -13X + 2X2 + -2X2

Combine like terms: 6 + -6 = 0
5 + -9X + -2X2 = 0 + 13X + -13X + 2X2 + -2X2
5 + -9X + -2X2 = 13X + -13X + 2X2 + -2X2

Combine like terms: 13X + -13X = 0
5 + -9X + -2X2 = 0 + 2X2 + -2X2
5 + -9X + -2X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
5 + -9X + -2X2 = 0

Factor a trinomial.
(1 + -2X)(5 + X) = 0

Subproblem 1
Set the factor '(1 + -2X)' equal to zero and attempt to solve:

Simplifying
1 + -2X = 0

Solving
1 + -2X = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2X = 0 + -1
-2X = 0 + -1

Combine like terms: 0 + -1 = -1
-2X = -1

Divide each side by '-2'.
X = 0.5

Simplifying
X = 0.5
Subproblem 2
Set the factor '(5 + X)' equal to zero and attempt to solve:

Simplifying
5 + X = 0

Solving
5 + X = 0

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

Add '-5' to each side of the equation.
5 + -5 + X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + X = 0 + -5
X = 0 + -5

Combine like terms: 0 + -5 = -5
X = -5

Simplifying
X = -5
Solution
X = {0.5, -5}