(2x+1)(-x+3)=0

Solution for (2x+1)(-x+3)=0 equation:

Simplifying
(2x + 1)(-1x + 3) = 0

Reorder the terms:
(1 + 2x)(-1x + 3) = 0

Reorder the terms:
(1 + 2x)(3 + -1x) = 0

Multiply (1 + 2x) * (3 + -1x)
(1(3 + -1x) + 2x * (3 + -1x)) = 0
((3 * 1 + -1x * 1) + 2x * (3 + -1x)) = 0
((3 + -1x) + 2x * (3 + -1x)) = 0
(3 + -1x + (3 * 2x + -1x * 2x)) = 0
(3 + -1x + (6x + -2x2)) = 0

Combine like terms: -1x + 6x = 5x
(3 + 5x + -2x2) = 0

Solving
3 + 5x + -2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, -0.5}