5s^2+7s+2=0

Solution for 5s^2+7s+2=0 equation:

Simplifying
5s2 + 7s + 2 = 0

Reorder the terms:
2 + 7s + 5s2 = 0

Solving
2 + 7s + 5s2 = 0

Solving for variable 's'.

Factor a trinomial.
(1 + s)(2 + 5s) = 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 '(2 + 5s)' equal to zero and attempt to solve:

Simplifying
2 + 5s = 0

Solving
2 + 5s = 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 + 5s = 0 + -2

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

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

Divide each side by '5'.
s = -0.4

Simplifying
s = -0.4
Solution
s = {-1, -0.4}