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

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

Simplifying
(a3 + -2a2) + -1(3a2 + -4a) = 0

Reorder the terms:
(-2a2 + a3) + -1(3a2 + -4a) = 0

Remove parenthesis around (-2a2 + a3)
-2a2 + a3 + -1(3a2 + -4a) = 0

Reorder the terms:
-2a2 + a3 + -1(-4a + 3a2) = 0
-2a2 + a3 + (-4a * -1 + 3a2 * -1) = 0
-2a2 + a3 + (4a + -3a2) = 0

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

Combine like terms: -2a2 + -3a2 = -5a2
4a + -5a2 + a3 = 0

Solving
4a + -5a2 + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + -5a + a2) = 0

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

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

Simplifying
a = 1
Subproblem 3
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
Solution
a = {0, 1, 4}