5f^2+7f+2=0

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

Simplifying
5f2 + 7f + 2 = 0

Reorder the terms:
2 + 7f + 5f2 = 0

Solving
2 + 7f + 5f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(1 + f)(2 + 5f) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + 5f)' equal to zero and attempt to solve:

Simplifying
2 + 5f = 0

Solving
2 + 5f = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5f = 0 + -2

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

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

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

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