5y^2+3y-26=0

Solution for 5y^2+3y-26=0 equation:

Simplifying
5y2 + 3y + -26 = 0

Reorder the terms:
-26 + 3y + 5y2 = 0

Solving
-26 + 3y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-13 + -5y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-13 + -5y)' equal to zero and attempt to solve:

Simplifying
-13 + -5y = 0

Solving
-13 + -5y = 0

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

Add '13' to each side of the equation.
-13 + 13 + -5y = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -5y = 0 + 13
-5y = 0 + 13

Combine like terms: 0 + 13 = 13
-5y = 13

Divide each side by '-5'.
y = -2.6

Simplifying
y = -2.6
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-2.6, 2}