2z^2+3z+3=5

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

Simplifying
2z2 + 3z + 3 = 5

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

Solving
3 + 3z + 2z2 = 5

Solving for variable 'z'.

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

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

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

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

Subproblem 1
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
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 = {-2, 0.5}