4(z-3)(-z-6)=0

Solution for 4(z-3)(-z-6)=0 equation:

Simplifying
4(z + -3)(-1z + -6) = 0

Reorder the terms:
4(-3 + z)(-1z + -6) = 0

Reorder the terms:
4(-3 + z)(-6 + -1z) = 0

Multiply (-3 + z) * (-6 + -1z)
4(-3(-6 + -1z) + z(-6 + -1z)) = 0
4((-6 * -3 + -1z * -3) + z(-6 + -1z)) = 0
4((18 + 3z) + z(-6 + -1z)) = 0
4(18 + 3z + (-6 * z + -1z * z)) = 0
4(18 + 3z + (-6z + -1z2)) = 0

Combine like terms: 3z + -6z = -3z
4(18 + -3z + -1z2) = 0
(18 * 4 + -3z * 4 + -1z2 * 4) = 0
(72 + -12z + -4z2) = 0

Solving
72 + -12z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -3z + -1z2) = 0

Factor a trinomial.
4((3 + -1z)(6 + z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

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

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

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

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

Simplifying
z = 3
Subproblem 2
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

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

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

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

Simplifying
z = -6
Solution
z = {3, -6}