3(2-3x)(8x+3)=0

Solution for 3(2-3x)(8x+3)=0 equation:

Simplifying
3(2 + -3x)(8x + 3) = 0

Reorder the terms:
3(2 + -3x)(3 + 8x) = 0

Multiply (2 + -3x) * (3 + 8x)
3(2(3 + 8x) + -3x * (3 + 8x)) = 0
3((3 * 2 + 8x * 2) + -3x * (3 + 8x)) = 0
3((6 + 16x) + -3x * (3 + 8x)) = 0
3(6 + 16x + (3 * -3x + 8x * -3x)) = 0
3(6 + 16x + (-9x + -24x2)) = 0

Combine like terms: 16x + -9x = 7x
3(6 + 7x + -24x2) = 0
(6 * 3 + 7x * 3 + -24x2 * 3) = 0
(18 + 21x + -72x2) = 0

Solving
18 + 21x + -72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7x + -24x2) = 0

Factor a trinomial.
3((2 + -3x)(3 + 8x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 8x)' equal to zero and attempt to solve:

Simplifying
3 + 8x = 0

Solving
3 + 8x = 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 + 8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x = 0 + -3
8x = 0 + -3

Combine like terms: 0 + -3 = -3
8x = -3

Divide each side by '8'.
x = -0.375

Simplifying
x = -0.375
Solution
x = {0.6666666667, -0.375}