-5a^2(4a^2-5a+4)=

Solution for -5a^2(4a^2-5a+4)= equation:

Simplifying
-5a2(4a2 + -5a + 4) = 0

Reorder the terms:
-5a2(4 + -5a + 4a2) = 0
(4 * -5a2 + -5a * -5a2 + 4a2 * -5a2) = 0
(-20a2 + 25a3 + -20a4) = 0

Solving
-20a2 + 25a3 + -20a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(-4 + 5a + -4a2) = 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 '(-4 + 5a + -4a2)' equal to zero and attempt to solve:

Simplifying
-4 + 5a + -4a2 = 0

Solving
-4 + 5a + -4a2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1 + -1.25a + a2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.25a + -1 + a2 = 0 + -1

Reorder the terms:
1 + -1 + -1.25a + a2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.25a + a2 = 0 + -1
-1.25a + a2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.25a + a2 = -1

The a term is -1.25a.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25a + 0.390625 + a2 = -1 + 0.390625

Reorder the terms:
0.390625 + -1.25a + a2 = -1 + 0.390625

Combine like terms: -1 + 0.390625 = -0.609375
0.390625 + -1.25a + a2 = -0.609375

Factor a perfect square on the left side:
(a + -0.625)(a + -0.625) = -0.609375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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