6y^2-13y=-5

Solution for 6y^2-13y=-5 equation:

Simplifying
6y2 + -13y = -5

Reorder the terms:
-13y + 6y2 = -5

Solving
-13y + 6y2 = -5

Solving for variable 'y'.

Reorder the terms:
5 + -13y + 6y2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -13y + 6y2 = 0

Factor a trinomial.
(1 + -2y)(5 + -3y) = 0

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 2
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
Solution
y = {0.5, 1.666666667}