(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.
(1 + -2x)(3 + 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 '(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 = {0.5, -3}