2s^2=5s+3

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

Simplifying
2s2 = 5s + 3

Reorder the terms:
2s2 = 3 + 5s

Solving
2s2 = 3 + 5s

Solving for variable 's'.

Reorder the terms:
-3 + -5s + 2s2 = 3 + 5s + -3 + -5s

Reorder the terms:
-3 + -5s + 2s2 = 3 + -3 + 5s + -5s

Combine like terms: 3 + -3 = 0
-3 + -5s + 2s2 = 0 + 5s + -5s
-3 + -5s + 2s2 = 5s + -5s

Combine like terms: 5s + -5s = 0
-3 + -5s + 2s2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1s)' equal to zero and attempt to solve:

Simplifying
3 + -1s = 0

Solving
3 + -1s = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1s = 0 + -3

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

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

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

Simplifying
s = 3
Solution
s = {-0.5, 3}