(a-3)(a^2+3a+a)=0

Solution for (a-3)(a^2+3a+a)=0 equation:

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

Reorder the terms:
(-3 + a)(a2 + 3a + a) = 0

Reorder the terms:
(-3 + a)(3a + a + a2) = 0

Combine like terms: 3a + a = 4a
(-3 + a)(4a + a2) = 0

Multiply (-3 + a) * (4a + a2)
(-3(4a + a2) + a(4a + a2)) = 0
((4a * -3 + a2 * -3) + a(4a + a2)) = 0
((-12a + -3a2) + a(4a + a2)) = 0
(-12a + -3a2 + (4a * a + a2 * a)) = 0
(-12a + -3a2 + (4a2 + a3)) = 0

Combine like terms: -3a2 + 4a2 = 1a2
(-12a + 1a2 + a3) = 0

Solving
-12a + 1a2 + a3 = 0

Solving for variable 'a'.

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

Factor a trinomial.
a((-4 + -1a)(3 + -1a)) = 0

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 '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 3
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {0, -4, 3}