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

Solution for (2x+3)*(3x-1)=0 equation:

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

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

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

Multiply (3 + 2x) * (-1 + 3x)
(3(-1 + 3x) + 2x * (-1 + 3x)) = 0
((-1 * 3 + 3x * 3) + 2x * (-1 + 3x)) = 0
((-3 + 9x) + 2x * (-1 + 3x)) = 0
(-3 + 9x + (-1 * 2x + 3x * 2x)) = 0
(-3 + 9x + (-2x + 6x2)) = 0

Combine like terms: 9x + -2x = 7x
(-3 + 7x + 6x2) = 0

Solving
-3 + 7x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x)(1 + -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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-1.5, 0.3333333333}