0=2z^2+5z-3

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

Simplifying
0 = 2z2 + 5z + -3

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

Solving
0 = -3 + 5z + 2z2

Solving for variable 'z'.

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

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

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

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

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

Factor a trinomial.
(1 + -2z)(3 + z) = 0

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Solution
z = {0.5, -3}