2z^2=5z-2

Solution for 2z^2=5z-2 equation:

Simplifying
2z2 = 5z + -2

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

Solving
2z2 = -2 + 5z

Solving for variable 'z'.

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

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

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

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

Factor a trinomial.
(1 + -2z)(2 + -1z) = 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 '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {0.5, 2}