3a(4a^2-5a+12)=

Solution for 3a(4a^2-5a+12)= equation:

Simplifying
3a(4a2 + -5a + 12) = 0

Reorder the terms:
3a(12 + -5a + 4a2) = 0
(12 * 3a + -5a * 3a + 4a2 * 3a) = 0
(36a + -15a2 + 12a3) = 0

Solving
36a + -15a2 + 12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(12 + -5a + 4a2) = 0

Ignore the factor 3.
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 '(12 + -5a + 4a2)' equal to zero and attempt to solve:

Simplifying
12 + -5a + 4a2 = 0

Solving
12 + -5a + 4a2 = 0

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

Divide each side by '4'.
3 + -1.25a + a2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.25a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -1.25a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.25a + a2 = 0 + -3
-1.25a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.25a + a2 = -3

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 = -3 + 0.390625

Reorder the terms:
0.390625 + -1.25a + a2 = -3 + 0.390625

Combine like terms: -3 + 0.390625 = -2.609375
0.390625 + -1.25a + a2 = -2.609375

Factor a perfect square on the left side:
(a + -0.625)(a + -0.625) = -2.609375

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}