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
(-6 * 2z + z * 2z) + 5(z + -6) = 0
(-12z + 2z2) + 5(z + -6) = 0

Reorder the terms:
-12z + 2z2 + 5(-6 + z) = 0
-12z + 2z2 + (-6 * 5 + z * 5) = 0
-12z + 2z2 + (-30 + 5z) = 0

Reorder the terms:
-30 + -12z + 5z + 2z2 = 0

Combine like terms: -12z + 5z = -7z
-30 + -7z + 2z2 = 0

Solving
-30 + -7z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -2z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-5 + -2z)' equal to zero and attempt to solve:

Simplifying
-5 + -2z = 0

Solving
-5 + -2z = 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 + -2z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2z = 0 + 5
-2z = 0 + 5

Combine like terms: 0 + 5 = 5
-2z = 5

Divide each side by '-2'.
z = -2.5

Simplifying
z = -2.5
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 = {-2.5, 6}