5a^2(3a^4+3b+2)=0

Solution for 5a^2(3a^4+3b+2)=0 equation:

Simplifying
5a2(3a4 + 3b + 2) = 0

Reorder the terms:
5a2(2 + 3a4 + 3b) = 0
(2 * 5a2 + 3a4 * 5a2 + 3b * 5a2) = 0

Reorder the terms:
(10a2 + 15a2b + 15a6) = 0
(10a2 + 15a2b + 15a6) = 0

Solving
10a2 + 15a2b + 15a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(2 + 3b + 3a4) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(2 + 3b + 3a4)' equal to zero and attempt to solve:

Simplifying
2 + 3b + 3a4 = 0

Reorder the terms:
2 + 3a4 + 3b = 0

Solving
2 + 3a4 + 3b = 0

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

Add '-2' to each side of the equation.
2 + 3a4 + -2 + 3b = 0 + -2

Reorder the terms:
2 + -2 + 3a4 + 3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a4 + 3b = 0 + -2
3a4 + 3b = 0 + -2

Combine like terms: 0 + -2 = -2
3a4 + 3b = -2

Add '-3b' to each side of the equation.
3a4 + 3b + -3b = -2 + -3b

Combine like terms: 3b + -3b = 0
3a4 + 0 = -2 + -3b
3a4 = -2 + -3b

Divide each side by '3'.
a4 = -0.6666666667 + -1b

Simplifying
a4 = -0.6666666667 + -1b

The solution to this equation could not be determined.

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