0=x(16x+24)

Solution for 0=x(16x+24) equation:

Simplifying
0 = x(16x + 24)

Reorder the terms:
0 = x(24 + 16x)
0 = (24 * x + 16x * x)
0 = (24x + 16x2)

Solving
0 = 24x + 16x2

Solving for variable 'x'.
Remove the zero:
-24x + -16x2 = 24x + 16x2 + -24x + -16x2

Reorder the terms:
-24x + -16x2 = 24x + -24x + 16x2 + -16x2

Combine like terms: 24x + -24x = 0
-24x + -16x2 = 0 + 16x2 + -16x2
-24x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-24x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-8x'.
-8x(3 + 2x) = 0

Ignore the factor -8.
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}