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

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

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

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

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

Combine like terms: -3z + 25z = 22z
(-15 + 22z + 5z2) = 0

Solving
-15 + 22z + 5z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
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}