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

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

Simplifying
(2x + 3)(3 + -1x) = 0

Reorder the terms:
(3 + 2x)(3 + -1x) = 0

Multiply (3 + 2x) * (3 + -1x)
(3(3 + -1x) + 2x * (3 + -1x)) = 0
((3 * 3 + -1x * 3) + 2x * (3 + -1x)) = 0
((9 + -3x) + 2x * (3 + -1x)) = 0
(9 + -3x + (3 * 2x + -1x * 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}