0=-5z^2-3z+2

Solution for 0=-5z^2-3z+2 equation:

Simplifying
0 = -5z2 + -3z + 2

Reorder the terms:
0 = 2 + -3z + -5z2

Solving
0 = 2 + -3z + -5z2

Solving for variable 'z'.

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

Reorder the terms:
-2 + 3z + 5z2 = 2 + -2 + -3z + 3z + -5z2 + 5z2

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

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

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

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}