6(6+q)(4-q)=0

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

Simplifying
6(6 + q)(4 + -1q) = 0

Multiply (6 + q) * (4 + -1q)
6(6(4 + -1q) + q(4 + -1q)) = 0
6((4 * 6 + -1q * 6) + q(4 + -1q)) = 0
6((24 + -6q) + q(4 + -1q)) = 0
6(24 + -6q + (4 * q + -1q * q)) = 0
6(24 + -6q + (4q + -1q2)) = 0

Combine like terms: -6q + 4q = -2q
6(24 + -2q + -1q2) = 0
(24 * 6 + -2q * 6 + -1q2 * 6) = 0
(144 + -12q + -6q2) = 0

Solving
144 + -12q + -6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '6'.
6(24 + -2q + -1q2) = 0

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

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

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

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

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

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

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

Simplifying
q = 4
Subproblem 2
Set the factor '(6 + q)' equal to zero and attempt to solve:

Simplifying
6 + q = 0

Solving
6 + q = 0

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

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

Combine like terms: 6 + -6 = 0
0 + q = 0 + -6
q = 0 + -6

Combine like terms: 0 + -6 = -6
q = -6

Simplifying
q = -6
Solution
q = {4, -6}