4s^2+5s-26=0

Solution for 4s^2+5s-26=0 equation:

Simplifying
4s2 + 5s + -26 = 0

Reorder the terms:
-26 + 5s + 4s2 = 0

Solving
-26 + 5s + 4s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-13 + -4s)(2 + -1s) = 0

Subproblem 1
Set the factor '(-13 + -4s)' equal to zero and attempt to solve:

Simplifying
-13 + -4s = 0

Solving
-13 + -4s = 0

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

Add '13' to each side of the equation.
-13 + 13 + -4s = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4s = 0 + 13
-4s = 0 + 13

Combine like terms: 0 + 13 = 13
-4s = 13

Divide each side by '-4'.
s = -3.25

Simplifying
s = -3.25
Subproblem 2
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
Solution
s = {-3.25, 2}