2z^2-3=-z-2

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

Simplifying
2z2 + -3 = -1z + -2

Reorder the terms:
-3 + 2z2 = -1z + -2

Reorder the terms:
-3 + 2z2 = -2 + -1z

Solving
-3 + 2z2 = -2 + -1z

Solving for variable 'z'.

Reorder the terms:
-3 + 2 + z + 2z2 = -2 + -1z + 2 + z

Combine like terms: -3 + 2 = -1
-1 + z + 2z2 = -2 + -1z + 2 + z

Reorder the terms:
-1 + z + 2z2 = -2 + 2 + -1z + z

Combine like terms: -2 + 2 = 0
-1 + z + 2z2 = 0 + -1z + z
-1 + z + 2z2 = -1z + z

Combine like terms: -1z + z = 0
-1 + z + 2z2 = 0

Factor a trinomial.
(-1 + -1z)(1 + -2z) = 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 '(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 = {-1, 0.5}