(1+z)(5z-2)=0

Solution for (1+z)(5z-2)=0 equation:

Simplifying
(1 + z)(5z + -2) = 0

Reorder the terms:
(1 + z)(-2 + 5z) = 0

Multiply (1 + z) * (-2 + 5z)
(1(-2 + 5z) + z(-2 + 5z)) = 0
((-2 * 1 + 5z * 1) + z(-2 + 5z)) = 0
((-2 + 5z) + z(-2 + 5z)) = 0
(-2 + 5z + (-2 * z + 5z * z)) = 0
(-2 + 5z + (-2z + 5z2)) = 0

Combine like terms: 5z + -2z = 3z
(-2 + 3z + 5z2) = 0

Solving
-2 + 3z + 5z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1z = 0 + 1

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

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

Divide each side by '-1'.
z = -1

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

Simplifying
2 + -5z = 0

Solving
2 + -5z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5z = 0 + -2

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

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

Divide each side by '-5'.
z = 0.4

Simplifying
z = 0.4
Solution
z = {-1, 0.4}