3s=2s^2+1

Solution for 3s=2s^2+1 equation:

Simplifying
3s = 2s2 + 1

Reorder the terms:
3s = 1 + 2s2

Solving
3s = 1 + 2s2

Solving for variable 's'.

Reorder the terms:
-1 + 3s + -2s2 = 1 + 2s2 + -1 + -2s2

Reorder the terms:
-1 + 3s + -2s2 = 1 + -1 + 2s2 + -2s2

Combine like terms: 1 + -1 = 0
-1 + 3s + -2s2 = 0 + 2s2 + -2s2
-1 + 3s + -2s2 = 2s2 + -2s2

Combine like terms: 2s2 + -2s2 = 0
-1 + 3s + -2s2 = 0

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

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

Simplifying
-1 + s = 0

Solving
-1 + s = 0

Move all terms containing s to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + s = 0 + 1
s = 0 + 1

Combine like terms: 0 + 1 = 1
s = 1

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

Simplifying
1 + -2s = 0

Solving
1 + -2s = 0

Move all terms containing s to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2s = 0 + -1

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

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

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

Simplifying
s = 0.5
Solution
s = {1, 0.5}