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

Solution for (4z-6)(5-z)=0 equation:

Simplifying
(4z + -6)(5 + -1z) = 0

Reorder the terms:
(-6 + 4z)(5 + -1z) = 0

Multiply (-6 + 4z) * (5 + -1z)
(-6(5 + -1z) + 4z * (5 + -1z)) = 0
((5 * -6 + -1z * -6) + 4z * (5 + -1z)) = 0
((-30 + 6z) + 4z * (5 + -1z)) = 0
(-30 + 6z + (5 * 4z + -1z * 4z)) = 0
(-30 + 6z + (20z + -4z2)) = 0

Combine like terms: 6z + 20z = 26z
(-30 + 26z + -4z2) = 0

Solving
-30 + 26z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 13z + -2z2) = 0

Factor a trinomial.
2((-5 + z)(3 + -2z)) = 0

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

Simplifying
-5 + z = 0

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

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

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

Simplifying
z = 5
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {5, 1.5}