(a^3-2a^2)+(3a^2-4a^3)=

Solution for (a^3-2a^2)+(3a^2-4a^3)= equation:

Simplifying
(a3 + -2a2) + (3a2 + -4a3) = 0

Reorder the terms:
(-2a2 + a3) + (3a2 + -4a3) = 0

Remove parenthesis around (-2a2 + a3)
-2a2 + a3 + (3a2 + -4a3) = 0

Remove parenthesis around (3a2 + -4a3)
-2a2 + a3 + 3a2 + -4a3 = 0

Reorder the terms:
-2a2 + 3a2 + a3 + -4a3 = 0

Combine like terms: -2a2 + 3a2 = 1a2
1a2 + a3 + -4a3 = 0

Combine like terms: a3 + -4a3 = -3a3
1a2 + -3a3 = 0

Solving
1a2 + -3a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(1 + -3a) = 0

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 '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3a = 0 + -1
-3a = 0 + -1

Combine like terms: 0 + -1 = -1
-3a = -1

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {0, 0.3333333333}