5s-2=-3s^2

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

Simplifying
5s + -2 = -3s2

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

Solving
-2 + 5s = -3s2

Solving for variable 's'.

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

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

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

Simplifying
-2 + -1s = 0

Solving
-2 + -1s = 0

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

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

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

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

Divide each side by '-1'.
s = -2

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

Simplifying
1 + -3s = 0

Solving
1 + -3s = 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 + -3s = 0 + -1

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

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

Divide each side by '-3'.
s = 0.3333333333

Simplifying
s = 0.3333333333
Solution
s = {-2, 0.3333333333}