5z(z-6)+4(z-6)=

Solution for 5z(z-6)+4(z-6)= equation:

Simplifying
5z(z + -6) + 4(z + -6) = 0

Reorder the terms:
5z(-6 + z) + 4(z + -6) = 0
(-6 * 5z + z * 5z) + 4(z + -6) = 0
(-30z + 5z2) + 4(z + -6) = 0

Reorder the terms:
-30z + 5z2 + 4(-6 + z) = 0
-30z + 5z2 + (-6 * 4 + z * 4) = 0
-30z + 5z2 + (-24 + 4z) = 0

Reorder the terms:
-24 + -30z + 4z + 5z2 = 0

Combine like terms: -30z + 4z = -26z
-24 + -26z + 5z2 = 0

Solving
-24 + -26z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -5z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-4 + -5z)' equal to zero and attempt to solve:

Simplifying
-4 + -5z = 0

Solving
-4 + -5z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5z = 0 + 4
-5z = 0 + 4

Combine like terms: 0 + 4 = 4
-5z = 4

Divide each side by '-5'.
z = -0.8

Simplifying
z = -0.8
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 = {-0.8, 6}