4c^2+13c+10=0

Solution for 4c^2+13c+10=0 equation:

Simplifying
4c2 + 13c + 10 = 0

Reorder the terms:
10 + 13c + 4c2 = 0

Solving
10 + 13c + 4c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(2 + c)(5 + 4c) = 0

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

Simplifying
2 + c = 0

Solving
2 + c = 0

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

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

Combine like terms: 2 + -2 = 0
0 + c = 0 + -2
c = 0 + -2

Combine like terms: 0 + -2 = -2
c = -2

Simplifying
c = -2
Subproblem 2
Set the factor '(5 + 4c)' equal to zero and attempt to solve:

Simplifying
5 + 4c = 0

Solving
5 + 4c = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4c = 0 + -5
4c = 0 + -5

Combine like terms: 0 + -5 = -5
4c = -5

Divide each side by '4'.
c = -1.25

Simplifying
c = -1.25
Solution
c = {-2, -1.25}