-2a^2(9-a-4a^2)+4a^2(a^2-2a+3)=

Solution for -2a^2(9-a-4a^2)+4a^2(a^2-2a+3)= equation:

Simplifying
-2a2(9 + -1a + -4a2) + 4a2(a2 + -2a + 3) = 0
(9 * -2a2 + -1a * -2a2 + -4a2 * -2a2) + 4a2(a2 + -2a + 3) = 0
(-18a2 + 2a3 + 8a4) + 4a2(a2 + -2a + 3) = 0

Reorder the terms:
-18a2 + 2a3 + 8a4 + 4a2(3 + -2a + a2) = 0
-18a2 + 2a3 + 8a4 + (3 * 4a2 + -2a * 4a2 + a2 * 4a2) = 0
-18a2 + 2a3 + 8a4 + (12a2 + -8a3 + 4a4) = 0

Reorder the terms:
-18a2 + 12a2 + 2a3 + -8a3 + 8a4 + 4a4 = 0

Combine like terms: -18a2 + 12a2 = -6a2
-6a2 + 2a3 + -8a3 + 8a4 + 4a4 = 0

Combine like terms: 2a3 + -8a3 = -6a3
-6a2 + -6a3 + 8a4 + 4a4 = 0

Combine like terms: 8a4 + 4a4 = 12a4
-6a2 + -6a3 + 12a4 = 0

Solving
-6a2 + -6a3 + 12a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6a2'.
6a2(-1 + -1a + 2a2) = 0

Factor a trinomial.
6a2((-1 + -2a)(1 + -1a)) = 0

Ignore the factor 6.
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 + -2a)' equal to zero and attempt to solve:

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 3
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
Solution
a = {0, -0.5, 1}