(X+2)(2X-1)=0

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

Simplifying
(X + 2)(2X + -1) = 0

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

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

Multiply (2 + X) * (-1 + 2X)
(2(-1 + 2X) + X(-1 + 2X)) = 0
((-1 * 2 + 2X * 2) + X(-1 + 2X)) = 0
((-2 + 4X) + X(-1 + 2X)) = 0
(-2 + 4X + (-1 * X + 2X * X)) = 0
(-2 + 4X + (-1X + 2X2)) = 0

Combine like terms: 4X + -1X = 3X
(-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}