3z(z-6)=5(z-6)

Solution for 3z(z-6)=5(z-6) equation:

Simplifying
3z(z + -6) = 5(z + -6)

Reorder the terms:
3z(-6 + z) = 5(z + -6)
(-6 * 3z + z * 3z) = 5(z + -6)
(-18z + 3z2) = 5(z + -6)

Reorder the terms:
-18z + 3z2 = 5(-6 + z)
-18z + 3z2 = (-6 * 5 + z * 5)
-18z + 3z2 = (-30 + 5z)

Solving
-18z + 3z2 = -30 + 5z

Solving for variable 'z'.

Reorder the terms:
30 + -18z + -5z + 3z2 = -30 + 5z + 30 + -5z

Combine like terms: -18z + -5z = -23z
30 + -23z + 3z2 = -30 + 5z + 30 + -5z

Reorder the terms:
30 + -23z + 3z2 = -30 + 30 + 5z + -5z

Combine like terms: -30 + 30 = 0
30 + -23z + 3z2 = 0 + 5z + -5z
30 + -23z + 3z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
30 + -23z + 3z2 = 0

Factor a trinomial.
(5 + -3z)(6 + -1z) = 0

Subproblem 1
Set the factor '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

Solving
5 + -3z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3z = 0 + -5
-3z = 0 + -5

Combine like terms: 0 + -5 = -5
-3z = -5

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
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
Solution
z = {1.666666667, 6}