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

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

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

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

Multiply (3 + -2x) * (2 + 3x)
(3(2 + 3x) + -2x * (2 + 3x)) = 0
((2 * 3 + 3x * 3) + -2x * (2 + 3x)) = 0
((6 + 9x) + -2x * (2 + 3x)) = 0
(6 + 9x + (2 * -2x + 3x * -2x)) = 0
(6 + 9x + (-4x + -6x2)) = 0

Combine like terms: 9x + -4x = 5x
(6 + 5x + -6x2) = 0

Solving
6 + 5x + -6x2 = 0

Solving for variable 'x'.

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1.5, -0.6666666667}