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

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

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

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

Multiply (3 + -1x) * (1 + 2x)
(3(1 + 2x) + -1x * (1 + 2x)) = 6
((1 * 3 + 2x * 3) + -1x * (1 + 2x)) = 6
((3 + 6x) + -1x * (1 + 2x)) = 6
(3 + 6x + (1 * -1x + 2x * -1x)) = 6
(3 + 6x + (-1x + -2x2)) = 6

Combine like terms: 6x + -1x = 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}