[(2x-1)(x+2)]=0

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

Simplifying
[(2x + -1)(x + 2)] = 0

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

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

Multiply (-1 + 2x) * (2 + x)
[(-1(2 + x) + 2x * (2 + x))] = 0
[((2 * -1 + x * -1) + 2x * (2 + x))] = 0
[((-2 + -1x) + 2x * (2 + x))] = 0
[(-2 + -1x + (2 * 2x + x * 2x))] = 0
[(-2 + -1x + (4x + 2x2))] = 0

Combine like terms: -1x + 4x = 3x
[(-2 + 3x + 2x2)] = 0
[-2 + 3x + 2x2] = 0

Remove brackets around [-2 + 3x + 2x2]
-2 + 3x + 2x2 = 0

Solving
-2 + 3x + 2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 0.5}