(5-z)(5z-3)=0

Solution for (5-z)(5z-3)=0 equation:

Simplifying
(5 + -1z)(5z + -3) = 0

Reorder the terms:
(5 + -1z)(-3 + 5z) = 0

Multiply (5 + -1z) * (-3 + 5z)
(5(-3 + 5z) + -1z * (-3 + 5z)) = 0
((-3 * 5 + 5z * 5) + -1z * (-3 + 5z)) = 0
((-15 + 25z) + -1z * (-3 + 5z)) = 0
(-15 + 25z + (-3 * -1z + 5z * -1z)) = 0
(-15 + 25z + (3z + -5z2)) = 0

Combine like terms: 25z + 3z = 28z
(-15 + 28z + -5z2) = 0

Solving
-15 + 28z + -5z2 = 0

Solving for variable 'z'.

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

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 + -5z)' equal to zero and attempt to solve:

Simplifying
3 + -5z = 0

Solving
3 + -5z = 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 + -5z = 0 + -3

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

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

Divide each side by '-5'.
z = 0.6

Simplifying
z = 0.6
Solution
z = {5, 0.6}