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

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

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

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

Solving
12a + -8a2 + 4a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(3 + -2a + a2) = 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 '(3 + -2a + a2)' equal to zero and attempt to solve:

Simplifying
3 + -2a + a2 = 0

Solving
3 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2a + -3 + a2 = 0 + -3

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

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

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

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -3 + 1

Reorder the terms:
1 + -2a + a2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2a + a2 = -2

Factor a perfect square on the left side:
(a + -1)(a + -1) = -2

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}