2x(x^2+10x+24x)=0

Solution for 2x(x^2+10x+24x)=0 equation:

Simplifying
2x(x2 + 10x + 24x) = 0

Reorder the terms:
2x(10x + 24x + x2) = 0

Combine like terms: 10x + 24x = 34x
2x(34x + x2) = 0
(34x * 2x + x2 * 2x) = 0
(68x2 + 2x3) = 0

Solving
68x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(34 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(34 + x)' equal to zero and attempt to solve:

Simplifying
34 + x = 0

Solving
34 + x = 0

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

Add '-34' to each side of the equation.
34 + -34 + x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + x = 0 + -34
x = 0 + -34

Combine like terms: 0 + -34 = -34
x = -34

Simplifying
x = -34
Solution
x = {0, -34}