6(a+4)(a-7)=0

Solution for 6(a+4)(a-7)=0 equation:

Simplifying
6(a + 4)(a + -7) = 0

Reorder the terms:
6(4 + a)(a + -7) = 0

Reorder the terms:
6(4 + a)(-7 + a) = 0

Multiply (4 + a) * (-7 + a)
6(4(-7 + a) + a(-7 + a)) = 0
6((-7 * 4 + a * 4) + a(-7 + a)) = 0
6((-28 + 4a) + a(-7 + a)) = 0
6(-28 + 4a + (-7 * a + a * a)) = 0
6(-28 + 4a + (-7a + a2)) = 0

Combine like terms: 4a + -7a = -3a
6(-28 + -3a + a2) = 0
(-28 * 6 + -3a * 6 + a2 * 6) = 0
(-168 + -18a + 6a2) = 0

Solving
-168 + -18a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + -3a + a2) = 0

Factor a trinomial.
6((-4 + -1a)(7 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
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 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-4, 7}