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

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

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

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

Multiply (-3 + 2x) * (3 + x)
(-3(3 + x) + 2x * (3 + x)) = 0
((3 * -3 + x * -3) + 2x * (3 + x)) = 0
((-9 + -3x) + 2x * (3 + x)) = 0
(-9 + -3x + (3 * 2x + x * 2x)) = 0
(-9 + -3x + (6x + 2x2)) = 0

Combine like terms: -3x + 6x = 3x
(-9 + 3x + 2x2) = 0

Solving
-9 + 3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(3 + -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 '(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
Solution
x = {-3, 1.5}