2f^2+5f+3=0

Solution for 2f^2+5f+3=0 equation:

Simplifying
2f2 + 5f + 3 = 0

Reorder the terms:
3 + 5f + 2f2 = 0

Solving
3 + 5f + 2f2 = 0

Solving for variable 'f'.

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

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

Simplifying
3 + 2f = 0

Solving
3 + 2f = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2f = 0 + -3
2f = 0 + -3

Combine like terms: 0 + -3 = -3
2f = -3

Divide each side by '2'.
f = -1.5

Simplifying
f = -1.5
Subproblem 2
Set the factor '(1 + f)' equal to zero and attempt to solve:

Simplifying
1 + f = 0

Solving
1 + f = 0

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

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

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

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

Simplifying
f = -1
Solution
f = {-1.5, -1}