0=32x(3+2x)

Solution for 0=32x(3+2x) equation:

Simplifying
0 = 32x(3 + 2x)
0 = (3 * 32x + 2x * 32x)
0 = (96x + 64x2)

Solving
0 = 96x + 64x2

Solving for variable 'x'.
Remove the zero:
-96x + -64x2 = 96x + 64x2 + -96x + -64x2

Reorder the terms:
-96x + -64x2 = 96x + -96x + 64x2 + -64x2

Combine like terms: 96x + -96x = 0
-96x + -64x2 = 0 + 64x2 + -64x2
-96x + -64x2 = 64x2 + -64x2

Combine like terms: 64x2 + -64x2 = 0
-96x + -64x2 = 0

Factor out the Greatest Common Factor (GCF), '-32x'.
-32x(3 + 2x) = 0

Ignore the factor -32.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
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 = {0, -1.5}