2z^2=3-5z

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

Simplifying
2z2 = 3 + -5z

Solving
2z2 = 3 + -5z

Solving for variable 'z'.

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

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

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

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

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

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
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
Solution
z = {-3, 0.5}