2z(z-6)5(z-6)=0

Solution for 2z(z-6)5(z-6)=0 equation:

Simplifying
2z(z + -6) * 5(z + -6) = 0

Reorder the terms:
2z(-6 + z) * 5(z + -6) = 0

Reorder the terms:
2z(-6 + z) * 5(-6 + z) = 0

Reorder the terms for easier multiplication:
2 * 5z(-6 + z)(-6 + z) = 0

Multiply 2 * 5
10z(-6 + z)(-6 + z) = 0

Multiply (-6 + z) * (-6 + z)
10z(-6(-6 + z) + z(-6 + z)) = 0
10z((-6 * -6 + z * -6) + z(-6 + z)) = 0
10z((36 + -6z) + z(-6 + z)) = 0
10z(36 + -6z + (-6 * z + z * z)) = 0
10z(36 + -6z + (-6z + z2)) = 0

Combine like terms: -6z + -6z = -12z
10z(36 + -12z + z2) = 0
(36 * 10z + -12z * 10z + z2 * 10z) = 0
(360z + -120z2 + 10z3) = 0

Solving
360z + -120z2 + 10z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '10z'.
10z(36 + -12z + z2) = 0

Factor a trinomial.
10z((6 + -1z)(6 + -1z)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

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

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

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

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

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

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

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

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

Simplifying
z = 6
Solution
z = {0, 6, 6}