2a^3-90a^2-392a=0

Solution for 2a^3-90a^2-392a=0 equation:

Simplifying
2a3 + -90a2 + -392a = 0

Reorder the terms:
-392a + -90a2 + 2a3 = 0

Solving
-392a + -90a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-196 + -45a + a2) = 0

Factor a trinomial.
2a((-4 + -1a)(49 + -1a)) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 3
Set the factor '(49 + -1a)' equal to zero and attempt to solve:

Simplifying
49 + -1a = 0

Solving
49 + -1a = 0

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

Add '-49' to each side of the equation.
49 + -49 + -1a = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -1a = 0 + -49
-1a = 0 + -49

Combine like terms: 0 + -49 = -49
-1a = -49

Divide each side by '-1'.
a = 49

Simplifying
a = 49
Solution
a = {0, -4, 49}