4a^2(a-1)(6+a)=0

Solution for 4a^2(a-1)(6+a)=0 equation:

Simplifying
4a2(a + -1)(6 + a) = 0

Reorder the terms:
4a2(-1 + a)(6 + a) = 0

Multiply (-1 + a) * (6 + a)
4a2(-1(6 + a) + a(6 + a)) = 0
4a2((6 * -1 + a * -1) + a(6 + a)) = 0
4a2((-6 + -1a) + a(6 + a)) = 0
4a2(-6 + -1a + (6 * a + a * a)) = 0
4a2(-6 + -1a + (6a + a2)) = 0

Combine like terms: -1a + 6a = 5a
4a2(-6 + 5a + a2) = 0
(-6 * 4a2 + 5a * 4a2 + a2 * 4a2) = 0
(-24a2 + 20a3 + 4a4) = 0

Solving
-24a2 + 20a3 + 4a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a2'.
4a2(-6 + 5a + a2) = 0

Factor a trinomial.
4a2((-6 + -1a)(1 + -1a)) = 0

Ignore the factor 4.
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 '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 3
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {0, -6, 1}