3y^2-10y-13=0

Solution for 3y^2-10y-13=0 equation:

Simplifying
3y2 + -10y + -13 = 0

Reorder the terms:
-13 + -10y + 3y2 = 0

Solving
-13 + -10y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(13 + -3y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(13 + -3y)' equal to zero and attempt to solve:

Simplifying
13 + -3y = 0

Solving
13 + -3y = 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 + -3y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3y = 0 + -13
-3y = 0 + -13

Combine like terms: 0 + -13 = -13
-3y = -13

Divide each side by '-3'.
y = 4.333333333

Simplifying
y = 4.333333333
Solution
y = {-1, 4.333333333}