(5x^3+5x)(x^2+6)=

Solution for (5x^3+5x)(x^2+6)= equation:

Simplifying
(5x3 + 5x)(x2 + 6) = 0

Reorder the terms:
(5x + 5x3)(x2 + 6) = 0

Reorder the terms:
(5x + 5x3)(6 + x2) = 0

Multiply (5x + 5x3) * (6 + x2)
(5x * (6 + x2) + 5x3 * (6 + x2)) = 0
((6 * 5x + x2 * 5x) + 5x3 * (6 + x2)) = 0
((30x + 5x3) + 5x3 * (6 + x2)) = 0
(30x + 5x3 + (6 * 5x3 + x2 * 5x3)) = 0
(30x + 5x3 + (30x3 + 5x5)) = 0

Combine like terms: 5x3 + 30x3 = 35x3
(30x + 35x3 + 5x5) = 0

Solving
30x + 35x3 + 5x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(6 + 7x2 + x4) = 0

Factor a trinomial.
5x((6 + x2)(1 + x2)) = 0

Ignore the factor 5.
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 '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = 0 + -6
x2 = 0 + -6

Combine like terms: 0 + -6 = -6
x2 = -6

Simplifying
x2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}