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

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

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

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

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

Multiply (-3 + 2x) * (2 + x)
0 = (-3(2 + x) + 2x * (2 + x))
0 = ((2 * -3 + x * -3) + 2x * (2 + x))
0 = ((-6 + -3x) + 2x * (2 + x))
0 = (-6 + -3x + (2 * 2x + x * 2x))
0 = (-6 + -3x + (4x + 2x2))

Combine like terms: -3x + 4x = 1x
0 = (-6 + 1x + 2x2)

Solving
0 = -6 + 1x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -1x + -2x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Reorder the terms:
6 + -1x + -2x2 = -6 + 6 + 1x + -1x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
6 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
6 + -1x + -2x2 = 0 + 2x2 + -2x2
6 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -1x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1.5, -2}