5y^2-16y-52=0

Solution for 5y^2-16y-52=0 equation:

Simplifying
5y2 + -16y + -52 = 0

Reorder the terms:
-52 + -16y + 5y2 = 0

Solving
-52 + -16y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(26 + -5y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(26 + -5y)' equal to zero and attempt to solve:

Simplifying
26 + -5y = 0

Solving
26 + -5y = 0

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

Add '-26' to each side of the equation.
26 + -26 + -5y = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -5y = 0 + -26
-5y = 0 + -26

Combine like terms: 0 + -26 = -26
-5y = -26

Divide each side by '-5'.
y = 5.2

Simplifying
y = 5.2
Solution
y = {-2, 5.2}