(2X+1)(3-X)=6

Solution for (2X+1)(3-X)=6 equation:

Simplifying
(2X + 1)(3 + -1X) = 6

Reorder the terms:
(1 + 2X)(3 + -1X) = 6

Multiply (1 + 2X) * (3 + -1X)
(1(3 + -1X) + 2X * (3 + -1X)) = 6
((3 * 1 + -1X * 1) + 2X * (3 + -1X)) = 6
((3 + -1X) + 2X * (3 + -1X)) = 6
(3 + -1X + (3 * 2X + -1X * 2X)) = 6
(3 + -1X + (6X + -2X2)) = 6

Combine like terms: -1X + 6X = 5X
(3 + 5X + -2X2) = 6

Solving
3 + 5X + -2X2 = 6

Solving for variable 'X'.

Reorder the terms:
3 + -6 + 5X + -2X2 = 6 + -6

Combine like terms: 3 + -6 = -3
-3 + 5X + -2X2 = 6 + -6

Combine like terms: 6 + -6 = 0
-3 + 5X + -2X2 = 0

Factor a trinomial.
(-3 + 2X)(1 + -1X) = 0

Subproblem 1
Set the factor '(-3 + 2X)' equal to zero and attempt to solve:

Simplifying
-3 + 2X = 0

Solving
-3 + 2X = 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 + 2X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2X = 0 + 3
2X = 0 + 3

Combine like terms: 0 + 3 = 3
2X = 3

Divide each side by '2'.
X = 1.5

Simplifying
X = 1.5
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 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 + -1X = 0 + -1

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

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

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {1.5, 1}