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

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

Simplifying
4a(2a2 + -1a + 5) = 0

Reorder the terms:
4a(5 + -1a + 2a2) = 0
(5 * 4a + -1a * 4a + 2a2 * 4a) = 0
(20a + -4a2 + 8a3) = 0

Solving
20a + -4a2 + 8a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(5 + -1a + 2a2) = 0

Ignore the factor 4.
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 '(5 + -1a + 2a2)' equal to zero and attempt to solve:

Simplifying
5 + -1a + 2a2 = 0

Solving
5 + -1a + 2a2 = 0

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

Divide each side by '2'.
2.5 + -0.5a + a2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5a + -2.5 + a2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5a + a2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5a + a2 = 0 + -2.5
-0.5a + a2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5a + a2 = -2.5

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = -2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = -2.5 + 0.0625

Combine like terms: -2.5 + 0.0625 = -2.4375
0.0625 + -0.5a + a2 = -2.4375

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = -2.4375

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}